Trout don't spawn in lakes, but in moving water usually sometime in fall. Brown Trout spawn in slightly warmer water than Rainbows and Brookies in colder water usually, this eliminates most all natural cross breeding. Trout in lakes will form eggs/milt in early to mid Fall regardless of wether or not there's moving water to spawn in. If there isn't suitable spawning water (read: moving, cool enough, etc.), the eggs/milt will be reabsorbed by the trout's body, in late fall, making it fatter than a successfully spawning trout of the same age. The eggs/milt may never even get to a useable size, but they will be formed to some degree. BTW milt is the term for fish sperm. If there is suitable spawning water the males will go upstream 1st and find an area with pea sized gravel and current that isn't too slow or way too fast. When the females come up the males will dig shallow holes with there tails called Redds. Then the male will try to hurd a female over his redd and nip her until she releases her eggs and he will release his milt at the same time. The eggs and milt will fall into the redd and then he will shallowly bury them with a layer of gravel. Any eggs that don't get fertilized usually don't sink as fast and will drift further down stream. Rainbows especially will eat these unfertilized eggs, which is why salmon eggs can be so effective in fall. Some people think they get some extra hormones by eating the eggs in nature, but that these hormones break down in packaged Salmon eggs. I think this maybe right but hasn't been proven.

Tight lines,
Wade