Yes, this can all be made to work. But you will need one additional cable s to connect all your fans' lights to the only mobo header available for them.
First, recognize this. These are "ARGB fans". Each is really two devices in one unit - a fan motor, and a set of lights. Each unit has TWO cables from it - one for the motor, and a separate one for the lights - and these plug into different places.
The LIGHTING units in all six of those Lian Li fans, plus those in the three rad fans of your AIO cooler system, are all the more advanced Addressable RGB (aka ADDR RGB, or ARGB) system. They require control and power from a THREE_pin (5 VDC power) Controller or mobo header. Your mobo has ONE of these it calls a Addressable Gen2 LED connector - see the manual on p. 1-26, and the location diagram on p. 1-2, key number 7. Do NOT attempt to use the FOUR-pin header right next to that! Now, just a load limit check. That header can supply up to 3 A current to all the lighting units connected to it. The web page info for the six Lian Li fans does not tell us the current each fan uses, but it does boast of 12 LED's per fan frame. That is more than most. The three fans for the rad on that AIO system does not even tell us that, but it won't be more. There is no info provided about any lighting connector for the pump of the AIO system. Now, the "rule of thumb" for these is that each LED needs at max 0.020 A. So nine fans at 12 LEDs each at that current comes to 2.16A max current, totally allowed from a single mobo ARGB header.
So how to get all fans' lights connected? We'll start with the Lian Li fans -six of them - that come with lighting connectors that are NOT the more common "standard" ones - instead they are a locking connector. That system also comes with a small hand-held manual Controller box you can use IF your mobo does not have what you need. But it does! The fans also include one adapter cable to deal with this. ( A little confusion: the manual for those fans comes as a .pdf file, and what I'm looking at is page 2 of that file. But at the bottom of that page is the number 3, because if it were printed out and folded, it would be p. 3.) At upper left under the heading "Motherboard Sync" is shows the use of ONE of the cables included with a 3-fan set that WILL plug into a standard mobo 3-pin ARGB header and then can feed three of those Lian Li fans' lighting connectors. So with two sets (6 fans) you will have two of those cables. Most of the other cables in the set are not needed for you - except the fan MOTOR cables (see below). So far you need two ARGB output connectors to plug in those six fans' lights.
On to the AIO system. It has three rad fans with lights that need power, and they DO have the "standard" connectors on their lighting cables. It also comes with an ARGB SPLITTER cable that can convert the single mobo header into four outputs - leaves one unused. Unfortunately, your case fans need TWO. So you need a different ARGB Splitter with FIVE outputs, like this
https://www.amazon.com/Cooler-Maste...&keywords=ARGB+Splitter&qid=1616119858&sr=8-6
Use that to go from the mobo header to the three rad fans, and then use its two extra outputs to plug in the adapter cables from the Lian Li 3-fan groups. Presto! Nine fans' lights fed and controlled from one mobo ARGB header, and all of them controlled using the ASUS Aura Sync software tool.
Now to the fan MOTORS - and remember, these have their own separate cables. These have a slightly different thing to consider, although they all do need power and control from mobo fan headers. The mobo has two similar fan control systems with an important difference. One is for the CPU chip cooling, and it is guided in its automatic fan speed control work by a temperature sensor built into the CPU chip itself. Look in the mobo manual on p. 1-21, and there are TWO headers that are controlled this way, identified as CPU_FAN and CPU_OPT. A different temp sensor built into the mobo is used to guide the headers intended for case cooling fans, and these are called CHA_FAN1, 2, and 3. For the PUMP part of your system, there is a dedicated header called AIO_PUMP which is different in that its speed can NOT be controlled - it always runs the pump at full speed as it is designed to operate. There is the H_AMP header, like other fan headers but able to supply a higher current up to 3.0 A. FYI, your mobo also has one other fan header for a special purpose you do not need: W_PUMP, a high-current header with no speed control, used only for custom liquid cooling loops with heavy pump systems. So, we need to connect the fan MOTORS for the rad fans to the CPU_FAN header, the PUMP of that system to the AIO_PUMP header, and the six Lian Li case ventilation fans to the CHA_FAN headers (BUT see below).
Again we do some load limit checks. All of the standard fan headers can supply up to 1.0 A max current. Most modern fans consume 0.10 to 0.30 A max current. Unfortunately the AIO system web page does not tell us that detail for its rad fans, but that's a good rule. so we CAN connect all three of them to the single CPU_FAN header, and that cooling system comes with a three-output fan motor Splitter to do that. The Pump of that system is straightforward - it plugs into the AIO_PUMP header. (Note that this header has an important secondary function - it watches the speed signal it gets back from that pump and, if that ever fails, you will get a prominent warning and it MAY actually shut down your system even before the CPU's internal temperature sensor show high temps.)
The Lian Li case vent fans provide a small issue to handle. Their web page says max input current is 0.45 A per motor, quite a bit larger than most. So you can only connect TWO of these to a single normal fan header IF you are using a SPLITTER. Those fan sets actually include a small circuit board (see first page of its manual) that functions like a Splitter and has six outputs from a single input. So you have the means to connect all six of those fans to a single mobo header, but that total max load is 2.7 A. Very fortunately your mobo has that H_AMP header that works just like any normal fan header but CAN provide up to 3.0 A. So THAT is where you connect the little circuit board (and thus all 6 Lian Li fans).
Lastly, some notes on how to configure the fan headers you use within BIOS Setup. See the mobo manual on p. 3-7, Q-Fan Control. On the left is a column of header labels, and NOTE that each header is configured separately using this screen. There are three important things you can adjust for each header. At upper right you can choose whether to use PWM Mode or DC Mode as the type of electrical signal sent out to the fan. In your case, set ALL of them to PWM Mode - that is best for 4-pin fan MOTORS , and all your fans are of this design. Across the bottom you can choose the fan PROFILE - that is, the strategy for deciding what speed the fan should run for any measured temperature. I strongly suggest using "Standard" for now. That will use a pre-set fan "curve" shown above in the graph. The next three options all are fixed fan speeds that do NOT change with temps. The last option, "Manual" allows you to set your own custom "fan curve" (see next page), and I suggest you not do that at least until you have some experience with the Standard settings. It is NOT shown on this illustration, but SOME fan headers also offer you a different option to select which temperature sensor is to be used for the header you are configuring. Usually there is no such choice for the CPU_FAN header, but there may be for the CHA_FAN and H_AMP headers. If so, ensure it is set to use the temp sensor on the mobo, not the one inside the CPU. When you have all the headers configured, use ESC at lower right, then the F10 key to get to the Exit Menu (p. 3-25). Choose Save Changes and Reset to save your settings and reboot.