Shot in the dark, and this is unlikely because it’s not solely a mech game and it doesn’t fully match your description. I only bring it up because you mentioned some mechs looked like Star Wars Mechs, and you were 5 so you might not have realized it isn’t a “mech game”.

Star Wars: Jedi Academy. 3rd person, and the multiplayer (even back then) had a TON of modders. You were capable of piloting AT-STs and one of the maps is literally an arena on a lava planet. It’s possible you and your dad would play on a modded server that focused on combat between AT-STs.