Don’t try it! It’s not worth it.
You may be able to recover a large, plain-profile tip with a green grit (silicon-carbide) wheel or a diamond hone for general sliding and surfacing cuts; but the more sophisticated tips including those for parting are moulded to sophisticated shapes of very high precision and accuracy for repeatable, efficient and high-finish production.
Parting-tool tips are also made with a cutting-edge that should be parallel with the lathe axis with proper machine-setting, and a central, symmetrical Vee-groove that folds the chips inwards to reduce binding and to face the cut surfaces properly.
Once a tungsten-carbide tip loses its edge it is effectively dead. It is not made to be re-ground, though you might be able to recover the front face alone by using a high-grade tool-and-cutter grinder with a diamond or Si-C wheel. Yes the manufacturers want to sell more tips, but they recognise the short life by stating expected tool lives in their catalogues; though admittedly for high industrial production in optimum conditions – including the right tool for the metal.
A heavy lathe might barge its way with light cuts through small-section material with an imperfect tool, HSS or carbide, if you are not too fussy about dimensions and finish, but the more lightly made machines really do need proper attention to tool geometry and setting for best results within their capacity.