Mamya, That explanation occurred to me too, but I rejected it. To me, for example, "he leant towards that view" indicates "inclined" to it, but not " advanced" it, or embraced it.
Chambers gives a meaning of "leant" as "to rest sideways against something".
It is possible to lean backward, too, as well as forward and sideways.
I don't think "leant" for "advanced" works.