currently(as of occultism 1.13) the lumberjack leaves all fruits on the ground including apples from oak trees.

Suggest to add items in the forge:fruits item tag to the list of items he will pick up. This should cover most modded fruits as well.

Hmm, forge:fruits is already in the list of items / has always been.
I'll have to look into why he's ignoring them

Edit: forge:fruits is a convention, but not default forge tag and thus empty. Adding apples by default in next patch.