514.1. First, if the active player’s hand contains more cards than his or her maximum hand size
(normally seven), he or she discards enough cards to reduce his or her hand size to that number.
This turn-based action doesn’t use the stack.

514.2. Second, the following actions happen simultaneously: all damage marked on permanents
(including phased-out permanents) is removed and all “until end of turn” and “this turn” effects end.
This turn-based action doesn’t use the stack.

514.3. Normally, no player receives priority during the cleanup step, so no spells can be cast and no
abilities can be activated. However, this rule is subject to the following exception:

514.3a At this point, the game checks to see if any state-based actions would be performed and/or
any triggered abilities are waiting to be put onto the stack (including those that trigger “at the
beginning of the next cleanup step”). If so, those state-based actions are performed, then those
triggered abilities are put on the stack, then the active player gets priority. Players may cast
spells and activate abilities. Once the stack is empty and all players pass in succession, another
cleanup step begins.

Give the Centaur Safeguard +1/+1 with Ursapine's ability, put a -1/-1 counter on it with Gnarled Effigy, pass to cleanup, Safeguard dies, triggers, cast Lightning Bolt targeting opponent in response to the trigger.

I didn't realize that "this turn" effects ended during the cleanup step. I knew it was possible to get the trigger on the stack after "until end of turn" stuff disappeared, but I thought "this turn" and "until the end of the turn" stuff were separate. I should have figured that out though, because now they use "until the beginning of the next end step" or something similar when they changed "at end of turn" to the new wording some years ago.