The mirtor thing id something I think is on the Gems, because Lapis herself said that they knew. I find a hard time believing they didn't know that Lapis was a Gem, but kept her like that cause they didn't know what frering her would unleash. This helps reason her actions against the gems because they were the ones who trapped her. Greg's leg being broken is a bit too indirect to place solely on Lapis. As for her telling homeworld, you forget she didn't mention Steven being Half-gem, plus you don't know what the Homeworld Gems could've done to her to get that information. Even if they did nothing, she had no reason to not tell Homeworld, especially since she never liked the Gems to begin with except for Steven. As for fusing with Jasper, that was twofold. First, she wanted to stop them, secind, she wanted to be left alone. Do you really think Garnet and the rest of the Gem's would leave her to her own devices, especially after what happened last time. She wasn't trying to win, she was trying to run and essentially commit suicide.