First check should be for twist in the bed of the lathe.
Check as per Ian Bradley "The Amateur's Lathe", or his "Myford Series 7 Manual"
This advocates what has already been suggested, or turning a "dumbell" and adjusting or shimming the Tailstock end of the lathe unrtil both ends of the dumbell are the same diameter.
Read through the thread posted by Robin, the method will probably be described there. The same problem is present.
Either that or use an Alignment bar, or even try making one.
Use Silver steel, of the largest diameter that will pass into the mandrel, (ideally 1" or 25 mm so that it is stiff ),
Ideally, mount in a 4 jaw chuck and clock to centre as accurately as possible.
If only a 3 jaw available, take a very light cut over a slightly longer length.
DO NOT CHANGE THE CROSS SLIDE SETTING. Preferably, lock it.
Mount with only a short length protruding from the chuck and centre drill. Repeat the light cut
Mark in line with a chuck jaw.
Reverse the Silver steel, end for end, with the mark in line with the chuck jaw, and centre drill.
Turn a longer length to the diameter of the first end.
Grip this longer end in the chuck,again with the mark in line with the chosen chuck jaw.
Set a clock on centre height and set to Zero on the turned section at the Headstock end.
Move it to the Tailstock end, on the turned section.
Shim, or adjust the Tailstock end of the bed until both readings are the same.
You have now taken the twist out of the bed, and can check the Tailstock.
Mount the bar between centres, and set the clock on centre height and Zero at the Headstock end. Adjust the Tailstock (there should be a screw, low down and facing you, and another at the far side of the Tailstock.
Adjust these screws until the clock reads Zero at both ends.
The Tailstock should now be aligned with the Headstock, in the horizontal plane.
Hopefully, it should be aligned in the vertical plane. To check, bring the Tailstock and Headstock centres so close that they grip a thick feeler gauge, or a steel rule. It should be held vertical by the centres..
Hopefully, the lathe will now turn parallel between centres or without.
But remember that long slender work will deflect under cutting forces, unless supported by a travelling steady.
HTH
Howard.