>What's preventing them getting cool water from a lake and draining to it again to cool down?
Some do, but most don't since the requirements for using cooling water are relatively strict due to the pipes, equipment, and heat exchangers the water flows through. The water used needs to be free of any biological contaminants (such as bacteria and algae), maintain proper pH levels, and are often then treated with other chemicals such as biocides.
Lake water certainly can be treated to the level needed and used, it's just often cheaper to buy domestic water from the local utility than to construct and operate a small scale water treatment system along side the industrial process.
> Where is water going after usage since there is literally zero water consumption?
Most of the water is "consumed" via open loop evaporative cooling systems, so the water is never really "used" as in destroyed or anything. The majority of it is evaporated and returns to the land as rain and the rest is returned via sanitary drains, to city sewer systems.