Depends. Your mileage may vary.
I will assume this current laptop doesn't have a dedicated GPU.
The processor inside that laptop is fine if you are looking at performance similar to an older budget gaming PC.
I would say your best purchase for an external GPU is to get an older GPU on the cheap that will be a match performance wise for that CPU.
Something like a 750ti or a 1050 2GB. (not a 1050ti, unless you are willing to pay the little bit extra for one.)
You of course would also need to invest into the eGPU adapter, whether it's just a PCIe adapter to plug it in and you buy a basic PSU to power it or you get an all in one option.
Otherwise, if you feel inclined to invest about $800 - $1,000 you can get a nice and affordable modern gaming laptop that will last you for quite a long while as long as you take care of it and do proper regular maintenance with keeping the entire cooling system free of dust build up to avoid overheating, throttling and overall the degradation of the hardware inside of it.
I can't recommend any sort of eGPU solution since I don't have the slightest clue as to what laptop you have and therefore I don't know what kind of connectivity solutions it offers for using an eGPU.
But as for a budget gaming laptop, I can refer you to these two different posts that will tell you what offerings are available and give you pros and cons to them to help you decide on one.
https://www.laptopmag.com/articles/sub-1000-gaming-laptops
http://www.ign.com/articles/the-best-cheap-gaming-laptops