Would the mud from the bottom of a lake be good in the garden?

Yes, great fertile soil.

No too much like clay

If the lake has supported fish for several years it would be great.

I'd imagine it'd be full of nutrients

According where the lake is located. In some deep south states the mud on the bottom of none flowing water sometimes contain some very deadly germs.

Check with local health officials first.

Would it not be mostly clay? Call or visit your local nursery to get more information for your area and project

Wow, what a variety of answers! Very interesting question!!!!

The bottom of the lake would contain a lot of run off from the ground, which would be silt and sand, which would not be ideal for a garden, low in nutrients. But as Deanna pointed out, lakes support aquatic life which would sink and fertilize the bottom or remain in a mixture in the water. Keep in mind that boats, ships and factories have left organic compounds. You also might want to consider the damage done by humans to the lakes with the garbage & debris.

Have you seen lakes where an area is closed off due to contamination from either chemicals or bacteria? Unsafe for swimming?

Generally, It would depend on the lake and the area where the bottom is being removed. Sounds like a good experiment!

Let us know how it turns out, best to you.