Only thing that comes to mind is, what is the neighborhood like? Not a real good chance that if you arrow a Lion on 5 acres it's going to die on that same 5 acres! What ever will the neighbors think?!?!?
I'm a huge fan of vocals, especially in tight quarters. Remote e-call ideally, but hand called whistling is also as effective, just keep still! It takes their sneak away. Calling distress is when they're going to "appear" sitting behind you watching the back of your head! Vocals often take off the sneak, and also can induce vocal response. BIG advantage!
Bow is very possible, I'd sure prefer shotgun with 00 Buck. But bow is ok if that's your only option. Sidearm recommended, but keep it as an afterthought, focus on what you're doing.
If sheep are consistently being killed, it's a super good opportunity.
If sheep are occasionally being killed, it's still an opportunity, but best to absolutely POUNCE on a kill report. Like minutes or hours, not days. Otherwise it's more like cold calling.
Not likely it's living there, unless it's killing every 4 or 5 days. If it's every 4 or 5 days, it's there, don't blow it while checking it out!
One other thing to consider, if it's there, it's very possibly a denning female. Most often a cat that won't leave is a denning female. If it's got cubs and it's taking sheep, call the Gamies.