I've found Lorentz's 1892 paper 'La théorie electromagnétique de Maxwell et son application aux corps mouvants' on Wikipedia (It's in French and I failed to find the English version.)
https://ilorentz.org/IL-publications/sources/Lorentz_AN_1892.pdf
However, I don't quite understand his derivation.Can someone help?
(The formulas for the Lorentz force are on page 443)