Peridot was just sending the droids to repair the warp pad (And later, to turn on the kindergarten).
I get the feeling Lapis Lazuli isn't really involved with the homeworld gems' plans beyond wanting to get home.
I originally thought Lapis had informed the home world gems of the crystal gem's survival. That would be the reason Peridot was sent to reactivate kindergarten. Otherwise, I can't think of a reason they home world gems would wait 6000 years to reinvestigate the earth. Of course there's also the chance Peridot isn't involved with home world and is working for another group.