I have only hiked out of Box Canyon and have never fished the Stillwater. I've never been to Lightning either, but I've hiked and fished all over the Lake Plateau. Osthoff's book Fly Fishing the Rocky Mountain Backcountry
says there are 12" rainbows in the Fork of the Stillwater. I've heard that Lightning still holds some very good goldens but the lake has been hammered by over use and camping. And there is a faint trail from the Stillwater up to Lightning but it's tough to find. Osthoff touts the Lake Plateau route going over Chalice Peak as being much better. There aren't really many lakes in the Lightning area other than Tumble Lake which is supposed to be tougher to get to than Lightning. Tumble is reported as holding very large cutts if you have the time.
If you do go to the Lake Plateau, my favorite lakes are Fish, Martes, Pentad, Jordan, and Pinchot. Martes is a trophy cutthroat lake and one of my favorite high lakes in all the Rockies. The best camping can be had at Fish and Pinchot. Wounded Man Lake appears to be a nice place to camp and fish, but bypass it in favor of Lake Pinchot. And whatever you do stay away from the Flood Creek Lakes. They are reported as having huge golden hybrids, but I went down in there last summer, and it was pure hell. The lakes do hold some good fish, but it was a bushwhacking nightmare to get to them, and they're almost impossible to fish due to super dense timber.
If you're taking a crack at the state record for goldens (or just targeting large goldens in general), check into Cave Lake in the Crazy Mountains. I've never been there but I am contemplating getting up there this summer. It's similar to Lightning in that it's eight very tough miles of hiking and stock cannot make it. The current state record came out of Cave. Cave is obviously no secret, but I've heard there is 5 miles of hiking on loose scree, which keeps 90% of the folks away.
I love this online guide for the Beartooths and the Crazy Mountains. http://fwp.mt.gov/fwpDoc.html?id=50253
Scroll down to Lightning for its fun facts. 16" goldens reported in 2003 and I found a random trip report online recently of a pair of guys holding up nice 14-18" goldens at Lighting. There is a seperate listing at the very bottom of the guide for lakes in the Crazy Mountains. You will find the awesome stats for Cave. 18-20" goldens
And if you're into trekking for monster brookies, PM me and we'll do some trading (for your Winds tips). The lakes are in the Beartooths but they're too far to hike from Lightning. Access is from trailheads on the southern portion of the range.