While I do not consider myself a finishing expert I do, nonetheless, have some experience in the area.
What you say you are seeking is really a paradox that likely can not be fulfilled unless you can find someone willing to give you, free of charge (or at least dirt cheap), a top of the line turbine (self contained) HVLP sprayer system...which could happen but seems unlikely!
To spray latex, especially unthinned, with an HVLP gun requires a large diameter tip (2.0+mm) and a
very large volume of sufficiently pressurized air. To get that volume of air in a turbine system while still maintaining the necessary pressure, a multiple-stage turbine system with a number of stages is required -- probably on the order of 4 or 5 stages if you are to have any chance of spraying unthinned, or at least minimally thinned, latex paint. Such self-contained turbine-based sprayers are at the very top of the line in turbine HVLP sprayers, so the requirement that it be cheap tends to rule such a solution out without a generous benefactor to donate one.
If you were opting for an air compressor driven HVLP gun and already had a compressor of adequate specs (or can secure one), then you could do so on the cheap as you would only need a suitable HVLP gun plus a large diameter tip and horn for it. Decent HVLP spay guns of this type can be obtained rather inexpensively. Plus you can adapt the spray gun to a wide array of jobs by purchasing a selection of spray tips and horns (1.0mm for touchups, 1.3mm, 1.7mm, and 2.0mm +/-) to match the intended finishes.
However, if this requirement to spray unthinned latex stems from a perception that an HVLP spray gun could be used to paint your next house then it is best to dispel that idea. For the money (on wasted paint) you would waste in overspray with an HVLP spray gun you could probably buy, and certainly rent, an
airless sprayer, which is the proper tool for the job if you are going to be covering a significant amount of surface area. At most an HVLP sprayer is potentially suitable for finishing trimwork or some cabinets with a latex finish, but no more. I mention this aspect because this often seems to be the thought process that leads many to tack on the "
unthinned latex" requirement to their list of criteria. Please ignore this paragraph if that was not your intent.
Best of luck in your search!