There's no practical way to get at the data on an LCII without a monitor, either an Apple one or a PC VGA monitor with an adaptor.
If you have a
Macintosh User Group in your area, one of the members might have a monitor that would work, or know where you can find one. A monitor that old would be virtually worthless, so you might be able to get one for free, or find someone who'll let you use it for a few days.
Otherwise, try eBay. Or Craigslist.
Even when you do get it up and running, you'll need an external floppy drive for the iMac, OR a modem or network card on the LC to transfer the file (unless you just want to retype it.)