Could be a random DDoS attempt, or trying to abuse some known or suspected vulnerability with connection attempts (like a buffer overflow that would cause the device to suddenly accept a login attempt from the outside to access the router's administrative interface so they could upload compromised firmware).
The manual is here and page 7 has the LED info, although they quite helpfully (/s) don't show a specific model and where the lights are physically so I can't say exactly what your model has.
https://www.lmi.net/wp-content/uploads/Gateway_User_Manual_v3_5.pdf
The WLAN light blinking sporadically could just be normal activity of an access point that is receiving signals/packets that aren't actually making a data connection, or that is just sending out the normal beacons, or maybe is doing a channel scan. I don't know about your device specifically and whether it would blink while a mobile device was trying to connect but didn't have the password, for example.
The Internet light blinking can mean the DSL authentication is in process, but that could be a slow blink or a fast blink, and might be very brief or might take a while. I have no experience with your device so really only you would be able to say if it was different this time. That light can also indicate actual traffic passing, so it could have been malicious coming from the Internet, or maybe the router was trying to do a firmware update. You have NO devices at home that would be connected when you're outside the house? No computer, no smart TV, no security camera? Nobody else in the house could have left a laptop or mobile phone behind when they went out?
Since you had no way to log into it to check on what devices may have been associated on the Wi-Fi, you've got no way to troubleshoot this. As
@USAFRet said, reset it, and create a long and strong password for the management interface and a long and strong password with a new wireless SSID. Hold the reset button for 6 to 20 seconds. Longer than that goes into a deeper reset mode. Note that you MAY need to contact your ISP to get the DSL connection configured again, unless you have the information sent to you when you signed up. The default credentials for the web interface are admin/admin.
If you want to be a little paranoid/security-conscious you can log in regularly and monitor for current associated devices, and the system and security logs (which likely don't go very far back) might catch association attempts or management login attenpts. Even knowing that someone did manage to crack your Wi-Fi password won't help you DO anything about it other than change the password and SSID every time, although you could configure it for a hidden SSID which makes it somewhat harder to break into.