What are the complete and exact rules that govern the epenthetic л in verb conjugations

It's inserted between a bilabial consonant (b, p, m, f, v) and j: люблю, куплю, кормлю, графлю, ловлю, but любит, купит, кормит, графит, ловит.

More importantly, what are the underlying phonological, etymological or historical rationales behind these rules ?

It's one of the manifestations of the law of rising sonority. It's not confined to the verb endings: земля < zemja, блюдо < biutta, Скопле < Skupi are all examples.

Other manifestation of this law, very closely related to the epenthetic l, is the iotation.

What are the complete and exact rules that govern the epenthetic л in verb conjugations

It's inserted between a bilabial consonant (b, p, m, f, v) and j (except before а): люблю, куплю, кормлю, графлю, ловлю, but любит, купит; любят, купят.

More importantly, what are the underlying phonological, etymological or historical rationales behind these rules ?

It's one of the manifestations of the law of rising sonority. It's not confined to the verb endings: земля < zemja, блюдо < biutta, Скопле < Skupi are all examples.

Other manifestation of this law, very closely related to the epenthetic l, is the iotation.