We have known lists of stars with high luminosity, temperature, mass, size, and much more. However, I have not seen a list that compares each star's mass loss rates. So, which star (or stars) have the highest mass loss rates, and is it going to be more likely to be an LBV, RSG, or a WR star?
Some very hot and massive stars have strong stellar winds, known spectroscopically as "P Cygni profiles" after the type star. P Cygni 'erupted' in the 17th century to magnitude 3 and is now visible as a mag.5-6 star near the central star of the 'Northern Cross' that is Cygnus. An ordinary pair of binoculars will show it easily. So P Cygni stars have probably the highest mass-loss rate as I believe you are thinking of.
It is my impression that some sort of supernova is likely to be losing mass at the fastest rate for a short period of time.
@fasterthanlight responded to my comment and sugggested that supernovae be ignored.
And there are a few rules applying to stars which are not having supernova events at the moment.
Stars tend to go through several phases or stages of development, and they tend to lose mass at different rates during different stages of development. If two stars start out with identical mass and composition but at greatly different times, and go through identical paths of development, their phases of development will be different at any one time, and so one may be losing mass faster at one time, and the other may be losing mass faster at another time.
As a star increases in mass, and thus the density, pressure, and temperature of its core, it requires more light pressure, produced by fusion, and thus more conversion of mass into energy and thus more mass loss, to prevent collapsing into a singularity.
So more massive stars fuse and convert into energy more mass per second compared to less massive stars. Of course more massive stars have more nuclear fuel to fuse than less massive stars. The math of the situation is that more massive stars burn off their fuel at a higher rate, relative to their total mass, than less massive stars as well as at a higher absolute rate.
So the more massive a star is, the more matter it will convert into energy each second both in absolute terms and as a proportion of its total mass.
Stars also lose mass by stellar wind, where charged subatomic particles in the atmospheres of stars flow outward from the star at great speeds. This varies a lot over the lifetime of a specific star, and varies a lot between various types of stars.
The Sun ejects more matter than normal during solar flares. Many small class M stars have much larger flares in absolute terms, and even more in relative terms, than the Sun and are called flare stars. So a flare star might eject less matter per second than the Sun most of the time, but eject more matter than the Sun during large flares.
Overall, as a rough guess, a super massive star at the upper mass limit for a star, and almost blowing itself apart, should lose more mass by conversion to energy per second while on the main sequence stage of its development than any other star on the main sequence. And if its mass loss at various stages of stellar development is proportional, then when it is at the star where typical star loses mass most rapidly it might be losing mass more rapidity than any other type of star.
Such super massive stars have many times the minimum mass necessary to become supernova, and so they should all eventually lose mas rapidly as supernovae.
However, it is certainly possible that astrophysical calculations will show that some other type of star at another stage of development might lose mass more rapidly.
For example, binary stars vary greatly in the distances between the two stars. Many orbit so closely that they almost touch.
If the two stars in a close binary have different masses, one will progress from stage to stage of development more rapidly and thus will swell up into a red giant star before the other one does. And as the red giant expands wider and wider, its surface may expand beyond the point where the gravity of the other star is stronger than its own gravity. Thus a lot of the material of the more massive star may leave it, and much of that matter may flow to the less massive star.
A star can lose mass very rapidly in such a situation.
So an astrophysicist should be able to select the type of star which loses mass at the fastest rate, and perhaps select the known example of such a star which is losing mass faster than any other star known at the present, although in many cases the data might be too uncertain.