Here's an excerpt from the introductory chapter of the LuaTeX reference guide (version 0.79.2):
Features may come and go. The current version of LuaTeX is not meant for production and users cannot depend on stability, nor on functionality staying the same. Nothing is considered stable just yet. This manual therefore simply reflects the current state of the executable. Absolutely nothing on the following pages is set in stone. When the need arises, anything can (and will) be changed. If you are not willing to deal with this situation, you should wait for the stable version. ... Full stabilization will not happen soon, the TODO list is still large.
In short, nobody in their right mind will assert that LuaTeX is "truly stable." That said, if your use case is mostly "plain vanilla" text typesetting (with little or no math) and if you use Opentype fonts, I'd say you can be reasonably sure by that no major instabilities will arise that may make working with Lua(La)TeX needlessly tedious. It's different for package writers. I gather, though, that your ambition isn't to create packages that exploit LuaTeX's many powers. Hence, you needn't worry about possibly having to modify features of your package to hide any "changes under the hood" from users.
By the way, some of the more significant changes that have occurred over the past three years are not related to the LuaTeX engine itself but to the
luaotfload packages. The good news, from my point of view, is that font loading and handling has become both much faster and more dependable over this period. For instance, the first time you run Lua(La)TeX on your system, a large font cache file is created; this used to take a rather distressingly long time just a couple of years ago, whereas now the task is typically accomplished quite expeditiously -- unless, I suppose, you happen to have several thousand fonts installed on your computer.
To be sure, not all changes have been for the best, at least not from my point of view. (I should mention that I use MacTeX on a system that runs MacOSX 10.10 "Yosemite".) In particular, starting with LuaTeX 0.78, support for Apple Advanced Technology (AAT) font features was dropped. While I can understand the rationale the Lords (no Ladies for now, unless I'm mistaken) of LuaTeX gave for this change, the upshot was that if your system runs MacOSX, some of the previously available font-related functionality -- e.g., kerning and ligaturing -- with some (though fortunately not most) system fonts vanished, poof!, without replacement when MacTeX2014 was rolled out.