I don't believe Ven lied there. We don't have the full picture what happened in there yet.

From what we know:
- Ava calls Ven to the warehouse
- Ven enters, it seems like no one is there
- Strelitzia enters, they see each over
- cut to Strelitzia lying on the ground; someone takes the manual
- Ven and Ava leaving the scene, Ven holds the manual

Also with Vens testimony(not clearly shown):
- Ava gave Ven the manual saying he should be the union leader and meet the others at the keyblade graveyard

My conclusion is that Ven and Strelitzia bumped into each other and talked. Ava entered after that and struck her down. (Possible after a talk between the three). She took the manual, the body vanishes (similar to Eraqus) and then she gave the book to Ven.

Alternatively Ava used Ven to do this and then altered/removed his memories.

*Note: with Ava in this thread I mean the Entity who appeared as Ava in Vens flashback. This could turn out as someone else in the future. But I believe it was her in person though