Hi Roger and welcome!!
No real rule as to whether to re-lacquer or not. Many people choose not to if the movement is under a glass dome or semi sealed case such as a anniversary, crystal regulator, carriage clock etc.
I was shown a great way to lacquer around 30 years ago by Joe Lyons of Lyons Clocks in Orange County, Ca. I don’t know if Joe is still in business now but he was a heck of a clock smith those days. I used to collect and deal in skeleton clocks a bit back then and although they were under glass domes I always lacquered them. My results were okay but always seemed a little dull and cloudy looking’. Whenever I would visit Joes shop I would check out his beautiful, superb, super clear and deep lacquer work. It was actually intimidating it was so good. I eventually got up the nerve to ask him his secret. His answer (not an exact quote but close) “Oh that? it’s easy, follow me”. He then led me outside to the side or behind his store (can’t really remember the layout of his shop) where he had a movement under glass sitting next to a can of lacquer which were both sitting in the sun! “Both the brass and the lacquer must be warm to hot and both must be the same temperature when the lacquer is applied or else you’ll get a cloudy finish with orange peel”.
I’m still here with no burns but ….Disclaimer: Please read any temperature warnings on can!! Heat at own risk.
It’s a simple process really. The plates should be super clean and then placed horizontally to apply the lacquer. Lacking sunshine you can always use a hair dryer.
Several very light coats will produce a beautiful deep finish. All lacquer must be removed from the oil sinks and from all pivot holes. If lacquer is left in the oil sinks the oil will run right out onto the plate so that step is Very important. I used to use regular lacquer until told about musical instrument lacquer. It’s made just for brass. As for the barrels and wheels I only did this with some skeleton clocks. I found that the process wasn’t usually worth the trouble.
You can also just wax the movement with a good carnuba car wax. Again, keep the wax out of the oil sinks if you go this route.
Hope this helps Roger,