Here's a helpful link:
http://www.greenhousegrower.com/varieties/lots-of-love-for-lofos/
It does mention "To make plants climb, some guides will be required." I interpret that to mean it's not a vigorous climber, at least not initially. =)

Lattice is relatively difficult for many plants to climb since the slats are so wide it's difficult for the plant to wrap tendrils around them. I've not grown lofos (Lophospermum) but you might try plant clips or ties to help the vine climb your trellis.

You don't say where you are, but this is a warm weather plant, and if your weather has been cool, it may be sulking a bit.