Does anyone know what size a lake has to be in order for stocked trout to live year long? I'd imagine depth plays a major role, but besides that, I am clueless.  I am pretty new to trout fishing, and have never caught a trout that wasn't stocked.
Lake: 25 acres.
Depth: 40 feet in certain areas.
I'm only asking this question to see if there may be some nice sized fish in a few years, or should I get used to the current stocked size? Any other info on these fish would also be greatly appreciated. Ie: habitat. Thanks in advance.

It depends on the lake they're being stocked in...as in how much Oxygen, water temperature, etc. Most of the lakes here in southern Ohio that get stocked with trout can't support them...so within a few weeks most die. However, there is one lake that they survive in, and we have caught 3 and 4 pounders there...so they are living just fine. Think it's the added Oxygen levels there, due to it being fed by several creeks and springs. It's hard to tell what will work best on your lake, but on ours we have good luck trolling Roostertail spinners and Jo-flies. When lures don't produce...we float Powerbait a few feet off the bottom...above a grass bed. Stockies get a bad rap from a lot of guys, but if that was all they had to fish for, maybe they would enjoy them as much as I do.
                                                                                                                                             

Well, you wouldn't believe the trout stocking programs California has. These large lakes and reservoirs get hundreds of thousands of trout stocked year round and many that are stocked are over 20 pounds. Hey, look it up. Personally, I hike up into the mountains and search for wild trout in out of the way creeks and rivers. Sure, they'll be smaller, but you won't have the "pay to fish" crowds, either. Just saying.

Thanks Mo. The fish in this lake will probably die out just like the ones by you. I'm in northern Ky so the climate is the same. This lake isn't stream fed or anything like that. Guess I'll just keep to the 2 to 4 pound test and enjoy it.
Troutinator. I have one small stream close to me, but the state stocks that also. I've caught my biggest trout out of there, but this time of year is catch and release only.

That sounds like a pretty good size lake. Im sure they could survive in it all year. U ask on how big they can get will my 2 cents is in a lake like that, their could be some 20 inchers in it, but it all depends on if they can grow that big. If the lake is overfished than the trout will get caught within a few weeks. Im sure some will get by. If there some big 1s in the lake anything natural to what they are feeding on will catch them.
Good luck and tight lines.

Im not familliar with lake specific situations but as a trout nursery manager in PA , there are many specific criterias such as water temp, PH, food resources, and species of trout. For example brook trout require much cleaner, cooler water than a rainbow or a brownie and have a much narrower water temp window as do the other said species plus that are much more subject to bacterias, gill disease, and have a low tollerance to PH changes. So i guess what im saying is that even though my information is not to your lake specifically im sure it applies as a general rule of thumb.