What possible conditions could lead to lizards developing into snakes and losing their limbs?

Plenty, living underground like worms, living aquatically like eels, living by poking through crevices like weasels (most limb-reduced, closest-thing-to-snakes among mammals), living by "swimming" through grass like skinks, living by shooting their heads out to catch fish like snake-necked turtles or "snaky" birds,,,,,,,

Lizards never turn into snakes.  I have seen a legless lizard, which has the physiology of a lizard but no legs; it burrows like a snake.

A snake has only one lung and is adapted very well to its legless condition.

A baby snake fossil  believed to be 98.8 Ma (million years) old was recently found.

The young snake’s bones were beautifully preserved in amber, a plastic-like material that was formerly tree resin. The fossil shows 97 vertebrae and ribs but the skull was not found. Some nearby shed snake skin fragments are assumed to be from the creature. However, there was no trace of hind legs or even a pelvis (hip), though these are known from certain ‘younger’ fossil snakes.

Applying standard uniformitarian/evolutionary reasoning to the fossil evidence as it stands, legs were lost, regained and lost again during evolution, but this violates an evolutionary precept called Dollo’s Law.

https://creation.com/baby-snake-fossil

https://creation.com/snake-evolution-story-stymied

there is an idea that   whales had feet ..they  had started living in water and eventually lost the feet because they didnt need them they still have  the  remnants of  leg bones

That is a nice hypothesis and fossil records show what would be snakes developed limbs for walking on land.

Predation 

Environmental factors 

Mobility advantages 

'All the better for giving you the slip!' 😉

"Losing their limbs" has happened more than once to lizards, in clades that use their noses to burrow.

Look up "glass snakes" and "legless lizards."

Fossorial life.

loads of mutations that don't stop them from procreating