Tommy7: If you are in an area that has gold, then yes, gold would make it to the lake although it will mostly be very very fine (powder to microscopic). Although larger gold would probably be present, You would have a couple of serious difficulties of retrieving it tho.
1) Lake bottoms are very silty. Gold settling in the lake would be very close to the inlet of the river/stream and will sink and get covered very quickly making any detectable sized gold hard to find with a MD. if you know gold is there, setting up a suction dredge and processing large volumes of sediment would be your best bet.
2) Gold Size. Most Detectors (at least mine) will not pick up gold smaller than about 1/8 inch unless very near surface and detcting very carefully.
If you are referring to a typical lake setting or a small "lake" in a stream/river (i.e. a large bend or ponded area) would affect your chances. A larger more developed lake will not provide a lot of chance for success (although Im sure it has been found). Small ponded areas where water slows and forms pools in the streams would offer greater chances for finding nuggets (under boulders, bedrock cracks, etc). If you are familiar with a sluice box, you know that sluices are designed to increase the flow of water in a confined path to essentially simulate faster flows you would experience during storm flow (although on much smaller scale) to remove gravels and sediment and leave gold behind. If youve ever seen one in action, the gold will usually be trapped at the first or second riffle. So, even during storm flows which can rip out huge amounts of material, larger gold does not necessarily move that far (but it certainly gets repositioned) which makes it great to prospect after a storm.
Typically, as gold progresses down stream/down gradient from its source, it gets beat up, flattened, rounded etc and gets smaller and smaller. Larger nuggets will not be found too far from source (usually). I would use metal detector along stream bank sides and hillside (benches, dips, cracks) combined with a little digging (to bedrock) in streams as well as gigging out exposed bedrock cracks on hillsides and panning to find evidence of gold. Then keep looking and work you way upstream to get closer to source and therefore larger nuggets. Also, keep eye out for nuggets that are less flattened/smooth and appear "coarser" as this is an indicator that the gold has not travelled as far (closer to a source). Most nugget and picker sized gold or coarse gold will be found within a few hundred feet down gradient of a vein or source location. further away than that, most gold will be various sized flakes or very small pickers. Most MD will not detect flakes unless in the larger picker or nugget size. Picker refers to a relative size large enough to pick up with your finger tips but not quite big enough to be considered a nugget
Sorry for the long winded reply, the gist of all this is that lakes are not (usually) that productive for small scale prospecting). I do most of my prospecting in Southern california/arizona. (not a whole lot of water, but we do get some nice storm flows!).
Good Luck!
Darren