How might water from a lake move through the water cycle and eventually fall as rain?

As the water vapor rises in the atmosphere it cools, forming tiny water droplets high in the sky by a process called condensation. Those water droplets make up clouds. If they grow large enough they eventually become too heavy to stay in the air, falling to the ground as rain, snow, and other types of precipitation.

The water vapor comes from anything that contains liquid which in this case, could come from a lake.

Is this alright or simpler explanation?

i believe you are right for all except the 3rd ( look at sqdancefan his answer is much better)