Least Significant Bit (LSB) vs Little Endian - Are they equivalent in anyway!
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).