Lost Phone - Can anyone connect new wifi from lock screen?

I lost my phone 2 days ago and someone turn it off before I got the chance to set Lost Mode (it now says pending). I know it will be in effect once it connected to the internet.

Now I wonder how my phone going to connect to the internet if he get rid of the SIM card? There's wifi. He can't get through the lock screen passcode. So can he connect to new wifi from the lock screen? Can he enter the wifi password from the lock screen?

By the way, I din't I set my Medical ID. So I guess the only way anyone can reach me from the phone is by turning on the Lost Mode.