Yeah ... on a wood lathe, it isn't nearly so critical to have the headstock perfectly aligned with the lathe bed and ways... for a wood lathe, merely having the headstock aligned with the tailstock is all that is required, and even then, it doesn't have to be perfect to still work perfectly fine.
First, make sure that the lathe is completely level .... a twisting of the lathe bed can cause that kind of mis-alignment easily.
Next, I would check the TAILSTOCK to see if the alignment can be adjusted from that end first .... if it cannot, THEN fiddle with the headstock.
After that, I'ld turn a test bar and see if things are "turning out all right" (pun fully intended). Just take a piece of scrap wood and turn a true cylinder (between centers) that is equally sized on either end (use calipers) .... swap it end for end and turn the lathe back on .... you will notice any wobble at all in the test bar if it is not perfectly aligned. The test bar is intended for testing how well the headstock and tailstock are aligned when they are NOT nearly touching ...
Now ... if there is wobble or not, turn the lathe back off (or do these next steps very deliberately and slowly, making sure not to let the tailstock slip back and let the test bar go flying) and unlock the tailstock ... shift it to the back (push it all the way back) and test for the wobble ... and then shift it to the front (pull it towards you) and test for wobble ... the lathe will probably align better in one of those positions.
If it doesn't, try keeping the lathe turned on and very gently and carefully moving the tailstock forwards and back till the wobble is as reduced as you can get it. Remember NOT to back the tailstock off ... just push it towards the back of the lathe and pull to the front WITHOUT pushing the tailstock to the RIGHT.
Once you've found the best position for alignment of the tailstock on the ways, you can lock it in position and mark the tailstock for the addition of shims on the lathe bed or tailstock bearing assembly to keep that alignment. Shims should be made of somewhat durable material, like brass or aluminum shim stock. Secure in place with a permanent adhesive, if you can.