Do I need a glasshouse?

No, we grow our loofah outside. In our climate growing in a glasshouse/greenhouse solves one problem but creates others so we choose to grow outside and have created a method for getting extra heat for outside growing.

Depending on your climate, if you're in a zone where the temps are cooler and the sunshine hours are lower then growing in a glasshouse may definitely be an advantage but keep in mind that luffa plants need lots of space and they will take over the whole glasshouse/greenhouse.