Are the steps to painting a plaster and lathe walls, house is early 1900's, the same as any other type of wall? What type of primer should be used? What type of paint? On the internet I read about the walls need to breathe and latex may prevent 'breathing' and moisture will build up.
On a home this old there will be layers of oil based paint and possibly additional layers of Latex paint. The biggest concern is good prep work (cleaning removing loose material) and a Quality paint. I have used both oil and latex on Victorian era homes with excellent results. It is really an opinion question today.
Old buildings were designed to breathe. Masonry used lime based mortar, and plaster used on lath is also lime based and porous. This meant there was flow of moisture in and out as temperatures etc changed. Using latex paint or any emulsion usually results in damp as it stops this breathability. Everyone then paints over damp patches with damp seal. This causes damp to rise (rising damp) etc etc.
If you're doing it properly, use a lime wash. You can mix up about 40 Litres (8 Gallons) for about £5. Lime wash is also breathable, and you can mix up your own quite nice colours using different materials (if you're keeping it traditional).
A good example is Kew Palace, London, which I'm pretty sure has been lime washed externally with the addition of brick dust to give it a nice orangey red colour. If using externally, mix in some linseed oil as it gives it some water resistance. Other options, are crushed coal dust for a black/grey (depending on ratios), or Westerham Sand for yellow.