I don't know who told you that, but don't do it! It was a rhetorical question, Lemi-shine is citric acid.
Using both or too much of one will leach zinc from your brass and turn it pink.
Technically, you could use both since they are the same thing, but you have to use such a small amount of either that that it would be hard to not use too much of each.
You use about 3/4 of a 9mm brass case full for a gallon.
The dish soap does the clesaning. The Lemi does two things...first softens the water which allows the soap to work better and of course it is what gives the shine to the brass, but it takes very little.