I do a Lake Trail run whenever I'm staying at The Breakers -- the trailhead on Sunset Ave. is roughly a mile from the hotel. The path runs right along the Intercoastal on one side and some of Palm Beach's priciest real estate on the other. Very pretty.
The course is flat, reasonably well-lighted, and easy to follow (although the end of the trail is somewhat unclear, as I couldn't see a sign or anything).
At the Sunset Ave. trailhead, there's a water fountain that actually has a chiller -- so the water is cold. Amazing (or perhaps not, given that it's Palm Beach). Although it would be nice if there was another fountain at the other end of the trail. Just a suggestion. ;-)
I recommend getting your run in early, especially if you're there in October like I was. Too sunny/warm otherwise.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.