In my opinion, 'She was leaned/leant over the table', 'The knife was lain on the table' and (except as a passive) 'The cat was sat on the table' are not standard English. The second is simply wrong.
Thank you very much for your kind reply.
I'm sorry but I'm not sure I can agree with you on your comparison with "to sit". According to many scholars, "to sit" is both a state verb (i.e. to be sitting down; to be on a chair or seat, or on the ground, with the top half of your body upright and your weight resting on your buttocks) and a dynamic verb (i.e. to sit down; to take a seat; to get into a sitting position somewhere after you have been standing up). I don't see "to sit" and "to lean" as cognates.
Moreover, the verb "to sit" can be both
transitive and intransitive. So, one can "sit somebody" (i.e. to put somebody in a sitting position) as in:
[transitive] sit somebody + adv./prep. to put somebody in a sitting position
He lifted the child and sat her on the wall.
She sat him down in front of the fire with a hot drink.
http://www.oxfordlearnersdictionaries.com/definition/english/sit
The above examples are in the active voice, and given that the verb "to sit" is used here transitively and that any transitive verb can be turned into a passive construction, then your example "The cat was sat on the table (by the girl)." should be correct.
As for the verb "to lean", please consider the following examples:
1. She was leaning over the table, trying to reach for her purse, when he came in. (movement implied as when he came in, she was in the act of leaning over the table)
2. She was leaned over the table, trying to reach for her purse, when he came in. (no movement implied as when he came in, she was already in that position)
I undestand what you all are trying to say and I am very grateful to all of you, but please note that the verb "to lean" has, among others, the following meanings:
1. To bend or slant away from the vertical. (as in my examples)
2. To incline the weight of the body so as to be supported: leaning against the railing. (as in Raymott's example in post #2)
As "to bend over" is a synonym of "to lean over", let's replace "lean over" above with "bend over":
1. She was bending over the table, trying to reach for her purse, when he came in.
2. She was bent over the table, trying to reach for her purse, when he came in.
http://idioms.thefreedictionary.com/lean+over
However, this is how I understand the examples I provided above. I am just trying to understand these constructions better. I might be wrong and that's why I am asking for your kind support. Thank you for your patience and help.