I tune my 12-string D-G-C-F-A-D. . Will this tuner do that?

With the Chromatic setting it will work with any tuning.

Will this tuner work to tune a 6 string electric lap steel guitar?

The tuner should work fine on the lap steel guitar

Does anyone know if this will tune a 12 string electric?

Yes it will tune a 12 string guitar when you use the Chromatic mode.

What the battery life? And what kind?

The included CR2032 battery life is ment to reach 1 year if kept in temperatures 22℃-27℃. This could be longer or less depending on how often you use it.

What are the dimensions of this tuner?

Clipped on the guitar it has a depth of 2″ (tuner plus clamp). The tuner itself is 2″ high x 1.25″ wide x about 1/2″ thick.

Does this tuner work well with solid body electric guitars?

Yes this tuner works well with solid body electric guitars.

Will it tune a delcimer?

Yes, it has a setting for chromatic tuning. As long as you can clip it on.