Henry Smoot,
The number style with the large curl on the 2, as well as the lettering, is quite similar to what is seen on several varieties of Rev War British and American buttons. However, I have not seen a 2 over LP in my years of collecting. There is a crown over RP (Royal Provencials), and I have even found one of those myself near Charleston SC (eyeballed in fact). A further search through Military Buttons of the American Revolution by Don Troiani, brought no match for a 2 LP that I could find. Is this a pewter composition button, or brass/copper?
A photo of the back would be quite helpful in determining origin as well. Many of the British buttons had large iron shanks (loops), while the American Continental and State Militia pewter buttons were often cast with a pewter shank. Please also provide size measurements, to give an idea of the button diameter.
There were French troops in the Revolution also, and nearly all the French buttons are typically brass with a birdcage type shank (small dome shape cast into the back, with four openings for thread attachment). Seems as I recall, the buttons for French enlisted men nearly without exception, have an encircling detail almost like a wreath (there is a word for this French design, yet it escapes my memory at the moment). Additional there were Hessian (German) troops employed by the British. There may possibly be some styles of buttons worn by Hessians, that differ from the style of British regulars.
CC Hunter