I have finished several pieces of wood furniture with acrylic lacquer. Some of them are getting fingerprints, dust, etc on them. Besides using a simple duster, what product should be used to clean the lacquer surface? Would Windex Multi-Surface Vinegar be effective and safe?
Dusting and wiping with a dry duster remain the safest cleaning options so should be relied on as much as feasible.
Would Windex Multi-Surface Vinegar be effective and safe?
I'm sure it would be effective but safe is another matter. Without knowing the exact product you used and how it's made up* it's really impossible to know what commercial cleaning products would and wouldn't be safe.
Other than just using plain water warm soapy water is the safest wet cleaning option if you need to take cleaning one step further than wiping dry. The cloth used should be damp and not wet when applied, and ideally you should wipe the surface dry as you go. Since they're now available everywhere use a microfibre cloth rather than the old standby of a dry, lint-free cloth. Microfibre is far more effective.
I want to emphasise warm water here, not hot. Under no circumstances should an acrylic product be cleaned with hot water unless you know for sure that it can withstand high temperatures. Many acrylic-based formulations are highly sensitive to heat and can be damaged by exposure to it, to the point where they can become tacky, turn cloudy and/or bubble and peel from the surface.
*A product labelled as "acrylic lacquer" from different manufacturers can be very different things with completely different characteristics because the name isn't defined anywhere.
Most finish names have no legal definitions so the product can be nearly anything the maker wants it to be. The best (or worst depending on your perspective) example of this is "Tung oil finish" which is a finish all right but the most famous example, the original one to the market, contains no tung oil at all and apparently never has. How's that for truth in product labelling?