Can anyone help me identify the year of this bike? I'm asking because I plan on buying parts to fix it up. I'll have to order them off the internet since the local bike shop says they can't find parts this old.
The serial number on the front underneath the schwinn logo reads "LK554026"
Seek and ye shall find. Look through the catalogs and find the year. It looks to be early-to-mid '70's to me.
What parts are you looking for to "fix it up"? There is likely nothing except cables and housing that needs replacing. Varsities are build like tanks. If the derailers are shot, you can go with newer. I don't know what the LBS was talking about. There are lots of sources for replacement parts. They might have brushed you off because they don't want to deal with it.
To fix up a Varsity, you may spend a lot more than it is worth. If you are going to keep and ride it, that's fine.
If it is going to be fixed up for sale, don't bother.
I have a near-mint Schwinn Letour, '74 model and can't seem to give it away. It is a much better bike than the one you have posted.
Also, one of the things that is really helpful to know is the exact components that are on your bike. For that, always take the photos from the drive-side and make sure to show the brand and model of the derailers.
Helps to match up to the catalog.
Please don't take my comments negatively, I'm just being realistic. Fixed up, with the paint in that condition, it is a $50.00 bike. New tires, tubes cables and housing will cost more than that. And it still will need all the mechanicals lubed.