I am not finding anything definitive, but I seem to recall the LaserJet's all being able to emulate an Epson FX series dot matrix, even graphics, so it MAY be possible to get decent output on a LJ2 from an apple II application speaking Epson FX commands.
I would get a proper serial cable and plug it in and start trying different printer configurations to see if you can get any decent output from it. NOTE: You may have to hit continue/on-line/OK or whatever to get it to actually spit out the page after sending data to the printer, I seem to recall this the last time I hooked my Apple II up to my LaserJet4. However it should be noted I was only printing basic text listing of a basic program (PR#1 and LIST), I wasn't dealing with any drivers or printer languages, just raw ASCII.
EDIT: I KNOW you will get SOME kind of output from a Apple II on a LaserJet2 with the proper cable, its just a matter of what you need to print, raw text is fully doable, its just whether or not you can get it to print graphics that is up in the air.