Captured Caverns
Zanzetkuken, we need a section of wall dropped across that section of waterway in the southeast corner of this map image to cut off flow. Make it as tall as possible, and prepare it in the stone layers above out of natural stone slabs. Like this:
Looking north (front view, from exterior), the wall runs east-west
###########
#._______.#
#.#######.# - This can be any number of z-levels tall, depending on how much undug space there is above the proposed site, up to the number of z-levels between lake floor and cavern ceiling.
#____I____# - Ceiling of cavern
#.........# - last z-level of cavern
Looking East (side view), a cross-section of the designation.
#####
#._.#
#.#.#
#_I_# - Ceiling of cavern
..... - last z-level of cavern
Where #=wall, .=open space, _=floor, and I=a support linked to a lever.
Just make sure that the 7x1x(X=height) block that is rigged to collapse is supported only by the pillar, then link the pillar up and drop it into the lake. It should then be denying access to the lake for cavern-dwellers. If you can't make it tall enough to reach the ceiling, just make it tall enough to fill the lake and then build constructed walls across it.
Then just make sure there are absolutely no other ways to access the area. After that, dig out an area to pump water into the lake to keep it full so we have a decently permanent fresh water supply. There should be a pump at the current highest level of the lake (such that the pump itself would be underwater currently) built into the walls.
interior side ~~:%-_++:~~ Exterior side.
Where ~=water, :=fortifications, _=a floor tile, %- =a pump aiming into the cistern, and ++ =a raising drawbridge to keep nasty beasties out of the pump area when the tank doesn't need to be filled. Link the bridge to a lever and keep it closed and link the pump to a power train from above (because a dwarf operator would just drown.)
When the bridge is up, nothing will be able to get in and attack us. When down, the pump will refill the water cistern up to it's natural depth (and not drown us if you keep the pump on the same z-level as the water.)