I'll add my .02 to say stripping and recoating is a pain and expensive. I've done both - at home and pro blasting for older steel frames. The blasting process needs a pro - and it costs - and it is easy for a less-skilled pro to not do a good job. Even getting a cheap pro paint job is a cost. I had mine powder-coated, as I wanted to use it as a commuter. So, after being on the road a month, a plastic bag got blown into the rear derailleur, the derailleur got pulled into the spokes, and bam, I went down. AND, the dropout broke. It was a Campy dropout - this was a pretty nice 531 frame - but it WAS also old. So, that nice powder coat got messed up when I had to get new dropouts braized in.
At home: if you want to try stripping, maybe try one of the newer limonene (citrus) based strippers. No nasty hydrocarbon fumes. I'm not sure how well it would work on an OEM lacquer finish - but it isn't expensive. They work well on housepaint stuff, I use them at home for my diy work on my house.
I had another old steel frame I redid some years ago, and as it was a 2nd level quality to begin with, I just used some sandpaper to rough the surface and bought cans of spray paint. That was about 15 years ago, and that paint is still ok.