the will of Thomas cain (m Elinor Leece) is on line www.iomfhs.im - summary:
3 surviving ch thos wm robt;all ua thos curghy uncle; 1770 thos caine chooses gfa wm leece & thos curghey as supv; 1779 thos & w ack from step father john kermod;wife ellinor + new husb (of renshant) petition

The Leece family had strong links with Liverpool and might well be the one you seek