Is it possible to request for vegetarian version of any of the dishes- like lasagna ?

Not that kind of place. There are other vegetarian options though.

Possible

There are many appetizers and pasta dishes without meat.

I don't think in the lasagna. But there's plenty of plates to select from the menu.

Unlikely as lasagna takes too long to make and it wouldn't be cost effective to make an entirely veggie lasagna for one person. I'd imagine they have great vegetarian options on the menu anyway so i wouldnt worry.

Nope