I messed up embarking and I do not have a river available for water. There are lakes I want to drain water from the bottom (I'm inside a mountain) and transport it to a hospital. Is there a way I can safely do this? I'd rather not dig downwards to pump up water. I don't want to learn how to use pumps yet and I've already dug 40 z levels down without finding underground lakes.
For moving water down, the right way to do that is with pumps or a large reservoir* that will not overflow (if the lake is 20 tiles then your reservoir must be at least 20 tiles at or below the level you wish the water to be at). To move water up, you will need a pump stack. To move water horizontally just build a tunnel (digging it 1 level below the water will help with the speed, due to pressure. You can also use buckets - designate a pond activity zone over a downward shaft and have dwarves carry water there.
Note that still water can be stagnant, in which case it will lead to unhappy thoughts and infections (while cleaning wounds), you can purify stale water by pumping it.
You really shouldn't be shy of using pumps - they only require 2 units of wood and 1 unit of stone to build and can be operated manually if you don't have power.
If you are worried about pressure and don't want extra pumps, there is a bug you can exploit - pressure does not travel diagonally, so you can just dig a shaft from the lake to the level you need the water at, then make a diagonal tunnel for water to travel through - it will not flow up. Here's an a top-down example.
wwww w=wall wwoo o=no wall ooww wwww
Not all sources of water have pressure. Only rivers source tiles, screw pumps and falling water into more are pressurised. So you only need the above cheat if one of these three sources of pressure occurs.
*Obviously a reservoir is not going to work if you are dealing with an infinite water source such as a river or an aquifer.
If you only want water for the hospital, and not for a water-based project, then you can do this easily without using pumps. A well will draw water up from below, no matter the distance, as long as there is nothing between them. It should be a simple matter to safely dig out a tunnel on the lake level to below where you want the well and move the water to there horizontally.
If you want to actually move water to form your own reservoir higher up, you'll either have to use pumps, or you can use activity zones, creating a water source and pond zones, to have your dwarves fill the pond with buckets.
If a lake is bowl-shaped, it can be hard to channel it into a tunnel at a level lower than the surface, but is definitely possible. I would break in a level above my tunnel, using grates on the floor and doors to give the dwarf an escape route when breaching the lake.