There are several ways to approach the lake. Since the approach from Cathedral Provincial Park in Canada is illegal (and logistically challenging), we'll rule that one out.
A lengthy, though scenic approach is from Horseshoe Basin. This also requires driving to Tonasket near the Canadian border east of the Pasayten Wilderness - a long drive from the Seattle area.
The next common approaches are from north of Winthrop, driving the Chewuch River Road. There are two trails leaving this road that will get you to Cathedral Lake: The Chewuch River trail and the Andrews Creek trail.
I followed the 100 Hikes recommendation of Harvey Manning and Ira Spring and hiked in via the Andrews Creek trail. This route takes you over scenic Andrews Pass and arrives at Upper Cathedral Lake - 21 miles and 4,900' gain later.
The first challenge was beginning my hike in the evening with plans to camp along the trail a short ways in. The valley is carpeted in downed trees and churned up rocks. There is no bare ground to be find until about 5 miles in. I found a nice, flat sandy area very near the former 5.5 Mile trail junction marker (the side trail has been obliterated - at least down low).
That being said, hiking over Andrews Pass, though mostly burned, was quite scenic. Historic Spanish Cabin was also a nice treat to visit.
Cathedral Lake is definitely the highlight of the area and the area to focus on. Don't forget Cathedral Pass.
The downside of beginning your stay here is that the other lakes won't impress. If Cathedral Lake is the dessert, the other lakes are more like the vegetables; Lower Cathedral Lake is down in a forested hole, and Remmel Lake is in open, rolling tundra with little supporting cast.
One thing I found out about the lake is that it has a LOT of fish in it, and towards evening they begin their feeding frenzy very near the shore, frustrating you if a wide-angle reflection shot is on your menu. Good luck with those jumping fish!
Another composition I wished to work was from the other side of the lake, looking back on Amphitheater Mountain. I never got the opportunity to do so though, as a system moved in, which I knew was forecast to stay awhile. I exited a day early, leaving this opportunity for another time.
While I wasn't impressed with Remmel Lake, there is a very scenic basin full of larch above it under the summit of Amphitheater Mountain on the south side. To get there, walk the trail back toward the Lower Cathedral Lake junction, and find the junction with trail #565. This trail stays mostly level as it traverses beautiful alpine country around the west shoulder of Amphitheater Mountain, before climbing up its gentle south slope up into this scenic upper basin.
As for wildlife, goats frequent the area and were regular visitors to my campsite. I never saw them though. They always visited during the night hours, and all attempts to rush out of my tent and catch sight of them with my headlamp proved futile. As soon as I got back in my tent, I could hear their hooves come racing back, likely hoping I had urinated somewhere close by.
Evening offers the best light for this area. The morning sun arrives late thanks in large part to Amphitheater Mountain running along the south side of the lake. The sun didn't hit my tent until shortly after 10:00 am.
I arrived at the TH and began my hike at 4:30 pm, with hopes of getting a few miles under my belt before sunset. I reached camp 5.5 miles in around 7:15, shortly after sunset.
The next morning I started out at 7:30 and hiked the remaining 14.5 miles to Cathedral Lake, arriving shortly after 2:00 pm. This gave me plenty of time to set camp and explore composition possibilities for that evening.
That evening, as expected, a system moved in after sunset (giving me great cloud action at sunset). I awoke to a dusting of snow in the morning, and icy cold conditions. Knowing the system was forecast to stay for a couple of days, and having nothing further to spend my day exploring, I decided to bail.
My final word of recommendation is to pack warm if visiting this area in the fall. At 7,400' elevation, Cathedral Lake is open to sudden changes in the weather, and the area can turn winter-like at a moment's notice.
Hindsight: It likely would have been safer to exit via the Chewuch River trail and hike the short road distance back to my vehicle.
I also wish I had explored the area around Apex Pass and the Tungsten cabins and mine. From Cathedral Pass, Apex Pass didn't look like much, and was at a lower elevation. I did not learn about the Tungsten cabins until after my return. Again, a reason to re-visit.
Finally, I'm glad I made visiting the Thirtymile Fire Memorial a priority during my visit (see previous post). I highly recommend you do too.