You might want to post this in the Pumpkins, Squash & Gourds forum, or the Vegetables forum.

Sure, you can try them on a trellis: maximizing the number of leaves on the vine is always good. If the variety bears
small fruit, you could try letting them hang from the trellis, watching carefully. Or you could play it safe and support the fruit in a sturdy sling hanging from the trellis. I believe I've read about cantaloupes hanging from slings. But larger pumpkins ... I'd want to keep the fruit on the ground.

Another possibility would be re-arranging the vines whenever they crawl onto the lawn.

Disclaimer: while I've grown pumpkins, I've never grown any on a trellis. However, I've grown many a cucumber on a trellis, and also some smallish gourds.

Ok, thanks. This is the problem with too many sub-forms, you get lost on where to post!

Only problem is I haven't ever used a trellis before, so I'll be doing something new all over again, haha.

I'll re-post in the proper section.

You are now discovering that sprawling vines and a mowed lawn are incompatible. What will you discover when you tie the vines up a trellis and the vines begin to fruit?

Sir Issaac Newton stopped growing pumpkins on trellises a long time ago.

...when he discovered it wasn't the falling; it was the hard landing.

Small vine varieties are fine for trellises, but the Jack-O-Lantern types would probably find any fruit snapping off at the stems for their sheer weight. Without the aforementioned sturdy slings, anyway.

Does your garden plot lend itself to your coaxing the vine to grow in circles around it? Sort of like a bad middle-aged hair day. You might not be able to keep multiple vines, but train one or 2. That way you have some scraggly lawn, but just in the perimeter of the veggie garden, & can maybe hand trim a little. Next year, try a different experiment!