Hunspell (GPL/mixed) is written in C++, and Java programs that use it normally use native access through BridJ/[JNA|https://github.com/dren-dk/HunspellJNA]. Jazzy (LGPL) is good, but not actively maintained, and simply looks up words from a dictionary.
We can provide a simple interface, and perhaps one or two different spell checkers in pure Java.
Having edit distances already in the project, we could investigate something such as adding a BK-Tree, an in-memory look-up spell checker, etc.
When creating the initial interfaces & design, it will be important to remember that we want to support multiple languages too.