We found the lamp being on/burning

[Ofriendragon]

When we got back from the cinema, we found the lamp _____ but the door _____.
A. being on; shut
B. burning; shutting
C. burning; shut
D. on; shutting
The answer is C.
Could you please tell me why A is wrong?
The following is what I am thinking about:
GroupA
1a. we found that the lamp was on
1b. we found that the lamp was burning.
GroupB
2a.We found the lamp being on.
2b.We found the lamp burning.

In Group A, I think both 1a and 1b are correct.
In Group B, both being on and burning are Object Complements. Why 2b is correct while 2a is wrong?

Please help me out and thank you in advance.

[Haihao]

If you want to take up 'on', you'd better drop 'being'. So A is not good.