The difference between the L15 and L21 series receptacles is the presence of a neutral wire, not a ground wire -- both types have a ground. The L21 series is intended for 3-phase Wye 120V/208V, whereas the L15 series is intended for three phase (either wye or delta) at up to 250V, where a neutral is not present or needed.
If your current L15 plugs are fed from a three-phase delta source, then without adding a new transformer, there's no way to get the netural wire you need for a L21 plug. However, if you have 120/208V three phase wye power, then you can simply run a new neutral wire back to your panel and switch the plug.
If, at your breaker panel, you have a neutral bus that's 120V away from all of the hot phases (check all three in case you have high-leg delta), then you have three phase wye power, and you can run a neutral wire and install an L21. If not, you probably have three phase delta, and will need a transformer to manufacture a neutral locally, if you really need to do that. If that's the case and you're interested in going that route, then report back here and we can try and help -- we'll also need to know what you're planning on powering from it.
Image source: https://www.belden.com/blog/data-centers/3-phase-power-wye-it-matters