It was handwritten. Several on this thread have made comments about the tense she used when she wrote "I could not take this Marine life"...vs. I can't...
This link indicates the military thought it matched her handwriting.
CNN
The handwriting appeared to match Lauterbach's, Sokoloski said. Durham also noticed some of Lauterbach's personal items and her car were gone.
However, civilian authorities began questioning it after she turned up dead. It's been sent out for handwriting analysis.
WRAL
The note from Laurean and the note Lauterbach left for her roommate have been sent to a handwriting expert for analysis, Sutherland said.
"We have received that (Lauterbach) note, and it's already been submitted to our crime lab. We don't have anyone here within our department that is an expert at analyzing handwriting," he said.
If it's fake, the killer left one too many clues back to himself. If it's real, it just supplements the story that she was upset and leaving.