Least Significant Bit (LSB) vs Little Endian - Are they equivalent in anyway! For a multiple choice question: What do we call the LSB?
(i)Little Endian    (ii)Upper bit   (iii)Big Endian (iv)Lower Bit

I feel ideally none of them is a true correct choice, but my best bet was (iv) Lower Bit.

However, our professor claims that the correct choice should be (i)Little Endian. He even said "LSB stands for Least Significant Bit which is right most bit of a binary equivalent and it is Little endian format."

I don't agree with the last part i.e. "..it is Little endian format."

My understanding (primarily from the book  “Computer Organization and Design” by Patterson and Hennessy,) is that LSB (and MSB) concepts were introduced to clearly identify bits at both extremes while avoiding any confusion arising due to writing styles like vertically or horizontally which can be confusing when read/written from different directions. Further it (LSB) has nothing to do with byte ordering such as Little endianness. For example any number will have both LSB and MSB, and can be stored in a little endian hardware as much as it can be stored in a big-endian hardware.

Pls let me know if I'm misunderstanding the professor's statement in any way.
LSB (least significant bit) and MSB (most significant bit) apply purely to the values of an integer. The least significant bit is the bit with value 1, the second least significant bit is the bit with value 2, and so on. 

"Little endian" and "Big endian" are just artefacts from the fact that the bytes of a number can be accessed individually as they are stored in memory. But if an integer is stored in 4 bytes, there are actually 24 different ways in which order these bytes could be stored in memory; big endian and little endian are just two of those 24. 

With all this said, if you have been understanding your professor correctly, and reported accurately what he said, then he is absolutely wrong. Actually the multiple choice answer "lower bit" is already nonsense (maybe not nonsense, but we really like precision in CS). If you have 32 bits, 31 of them are "lower" than some other bit, but ONE of them is the lowest bit. The Least Signficant Bit. 

When "Little Endian" and "Big Endian" are abbreviated, they are abbreviated as LE and BE (for example UTF-16 LE and UTF-16 BE).