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Lavatera is a large genus with a variety of species in cultivation; in addition, it is a member of an extensive family that include hibiscus, hollyhocks, mallow, and many others. This has led to confusion, because many of the flowers look much alike, so one plant is often called by the name of another one. Even among the lavateras there's quite a bit of variation in size and flower time.
This is one big reason you see differing pruning directions.
The other reason is that the plant is so vigorous that, when you come right down to it, it doesn't seem to matter much when you prune it. So one gardener will have good results pruning it in the fall, and another will have good results pruning it in the spring.
I think one thing that could possibly be a concern is winter. The sources I found list lavera as hardy only to zone 6 (-5F), so if your weather gets cold, you probably don't want to prune in the fall.
All that being said, if it were my plant, I would probably do heavy pruning in early spring, although if I needed to keep the plant to a certain size, I would prune back branches here and there throughout the summer.