Is it lowercase, lower-case, or lower case?
Warren Chappell, Robert Bringhurst, and the printed Unicode Standard all use lowercase exclusively.
The only exception is when sorts are kept in two cases, and one puts some of those in the lower one and others in the upper.
Lowercase initially came from "lower case", referring to literally the lower case of the cabinet where this typeset was kept by convention. It has gone through the typical contraction from "lower case" to "lowercase" via the hyphenated form. The use of the word (lowercase) has seen a spike in usage during the last decade or so, as everyone needs to know (now) that passwords are case sensitive and that using uppercase is shouting. Back in the days of the Guttenberg press, a lot of print was all uppercase. Fashions change, as do fontfaces.
All are okay--I've seen English teachers use all three, so it must be fine. I think it just depends, maybe, on where you live. In the United States and other countries, people use lowercase more often, but in other countries they might use lower case or lower-case most often. I'm pretty sure that it doesn't matter. All ways of writing it are okay. Since lowercase is used more often in the United States, it may be helpful to use lowercase, but if you live in someplace where most people use lower case or lower-case, you should probably use the way that people spell it where you live. Nobody will mind, most likely, and people will understand it all three ways, but if you spell it in a way that most people from where you live don't spell it, they may use it as bad grammar and it may not bode you well if you are doing something formal. Just try to spell it the way that most people from where you live spell it.