How much does it cost to deal with the tree is leaning now and it wasn't before?

The distinctive driver is that the tree's natural fall direction is already committed and probably points at the thing you are worried about, so it cannot simply be dropped. That forces a crane, a winch and pull line, or piecing it down from a bucket — all of which price above a straightforward felling. Soft, saturated ground adds cost too, since heavy equipment needs mats or plating to avoid rutting the lawn.