Is there a formula to calculate any star mass from Luminosity, Radius, and/or Temperature (K)?
I think the issue you are going to have here is that the position of a star in the HR diagram - which amounts to saying what the (2 dimensional) spectral type is - does not just depend on its mass.
The Vogt-Russell theorem says that the position of a star on the HR diagram depends on its mass, its composition and crucially, how its chemical elements are distributed in the interior. Thus we know for example that we could find a 2 solar mass star on the main sequence with a spectral type of say A2V but it is also possible for a K0III giant to be a star of 2 solar masses.
So there really isn't any shortcut or quick formula that is going to give you a route to finding the mass based on a spectral type (or equivalently, based on a luminosity and effective temperature).
If you know the star is on the main sequence then you can use an approximate luminosity-mass relation (although you should be aware that stars change their luminosity during their main sequence lifetime and so the luminosity of a main sequence star depends on its mass, age and its initial chemical composition).
If your star is a giant or at some intermediate evolutionary stage (subgiant, or some short-lived supergiant phase) then it is really difficult to estimate the mass of such an object without also knowing its age. For example if you know a giant star is a billion years old, then there is only a small range of masses which will be in the relatively short-lived giant phase at 1 billion years old.