Would the following Latin words: "Disce sub crux lumen" translate to the phrase
 "The light of learning under the cross" ? If not, what would be an
accurate Latin translation.

I wouldn't quite translate it that way. "Disce" looks like a verb form
of "discere" meaning "to learn", but it looks to be in an imperative
form, a command or request meaning "Learn."

I also don't think "sub crux" is grammatically correct, but if it were
"sub cruce" it would translate as "under the cross"

"Lumen" in indeed a word for "light" and I note that the phrase "sub
cruce lumen" is apparently the motto of the University of Adelaide in
Australia where it's taken to mean "The Light Under the Cross" where
"light" is a reference to eductation and "cross" is a reference to the
consteallation sometimes called the Southern Cross that's visible in
the Australian sky. (That constellation is sometimes called "Crux"
after the Latin.)  So "Sub Cruce Lumen" at a motto is sometimes taken
to mean "The Light (of Learning) under the Southern Cross".

Adding "Disce" to the phrase may be an attempt to add a clear
imperative element to the phrase such as "Learn from the Light Under
the Cross" or even "Learn at the University of Adelaide" but if so,
the grammar isn't exactly right to make those translations
self-evident.

"Lux discendi sub cruce" is the correct and literal translation.