Unless the cavern is secured, a well above the lake provides a means for fliers (and possibly climbers) into the fortress. Thus, a safer way, when you've got time, is to build a cistern and lead water from the lake into it via an airlock (two raising drawbridges with space in between). You can also use a single drawbridge and a wall grate (which can be destroyed by building destroyers, and so isn't sufficient on its own). The cistern ought to be at least two tiles deep a the location where you draw water from it (i.e. the well and any water gathering zone).
If there is a path to the lake dwarves should take water from it provided the 'o'ptions for 'z'ones haven't been set to take water from zones only, without painting a water collection zone over (part of) the lake (and the edge of it).
If a dwarf is injured and resting in the hospital and starting to get dehydrated, but you don't have any water, you can try to remove the hospital zone (and deconstruct a traction rack, if the dorf is in a rack). This will wake the dorf up and may make it go/craw to get a drink or healthy booze. You can then put the dorf back into the rack when the thirst is sated. I had to do that on a map completely devoid of water, and after 3-4 sessions the injured dorf had actually recovered enough to be able to work again.