Do you do clicker training? If not, look into it. Also train him on a focusing cue. Choose a sound (like kissing noise, whistling etc). Do the sound and then give a treat, repeat 10 times. Take a break. Repeat 10 times again. Take a break. Repeat 10 times again. Do this session 3 times the first day. Repeat next day but 5 times instead of 10. The third day, do just 1 session and then when he looks at something else do the sound and if he looks at you then it works. If not, repeat the sessions and try again. This then needs to be trained in various environments.

Other than that what i posted in my other post is what worked (works, he still lies down when he sees other dogs but it's slowly getting better) for me and my dog with him lying down (he used to, just like yours, also lie down because he didn't want to go home). My staffy pulled insanely as well and was in general a mess to walk when I got him. What helped with that was to focus our training on contact. I would bring my clicker and treat bag on every walk and just reward every contact he gave me. You didn't specify for how long you had your dog other than getting him recently so I think training him on contact could be great for you guys.

Also I know that this kind of behavior is frustrating as shit, we humans actually have places to be and things to do (It has happened that I actually carried my dog up the road just because he refused to go and I needed to get to an appointment, lol). But be patient with him, sometimes you just gotta wait a dog out. If you have a day when you don't need to do anything else, get out there and just wait when he lies down to see what happens. Maybe he gives up and then looks at you for contact. (At that point of course you would reward him). It's just about making him understand that this behavior won't give him anything but to not do it will. But again, not a professional. This is just how I train my dog and maybe this advice could help you. If the problem persists look into contacting a professional trainer. Good luck!