I use Line and had the same issue. I tried everything and couldn't get Line to send the verification text. I just ended up contacting their support and after several days of responding to their repetitive questions, they just sent a code via email.
I seem to remember Line requires GMS. Something I literally just thought of right now is maybe temporarily adding both the "phone" and "sms" permissions to both Line and Google Play Services might work?
Adding the "phone" permission allows apps to view your phone number, among other things, so it's up to you if you'd like to try that. I won't try it myself because I have Line working and I'm not about to mess that up!