even still water has a slight current to it. but yes trout can spawn in lakes and ponds. sometimes it doesn't work out to the fishers advantage as trout don't usually stick around to protect the eggs like bass do and most still water lakes and ponds don't have the same gravel as streams to hide the eggs and other fish such as kivvies and growing younglings of other fish will feed on the eggs. this causes less trout eggs to hatch and grow into mature adults. but yes they will spawn in still water the same as streams and rivers just not always as successful.

Peersonally, I have never heard of trout spawning successfully in ponds, but I don't know it all.  Rainbows will try in the spring at any inflow point though.  Try your state fisheries people and the agriculture people in some states have info also