"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.

Both lower case and lowercase can be seen in common usage, but it seems that lowercase became more popular after 1980s. You may want to check the following ngrams.

The same case is valid for uppercase.

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.