Does TE buffer carry out RBC lysis? if yes then how? secondly if it has such an effect on RBCs then why does it not carry out WBC lysis?

RBC lysis is usually done by sudden changes in osmotic balance. The method I have done uses a binary salt solution, one low, one high. The cells are suspended in the low (hypotonic) salt solution first, which forces water into the cells by osmosis, making them burst. I'm not exactly sure why other cells are not as susceptable to lysis by this method, but I think it must be that they are simply more resistant to osmotic shock. After 30 seconds the high salt (hypertonic) solution is added, bringing the salt level in the buffer to isotonic levels (roughly 150 mM) and preventing further lysis. TE is a very low (hypotonic) salt solution, so I suspect it would quickly lyse RBC in sufficient volumes, though I have never tried it.

agreed with above - TE (TRIS and EDTA) is essentailly buffered sterile water that is hypotonic so will lyse RBCs. its main function is to stabilie DNA.