So what's a DDR3L (1.35V) SODIMM? I have no clue what the difference is between LPDDR and something like DDR3L, but you sound like someone knowledgeable enough to answer.
DDR3L is lower voltage but otherwise identical to DDR3. LPDDR is an entirely different line used mostly in cell phones. LPDDR3 has no relationship to DDR3, just as LPDDR2 had no relationship to DDR2 and LPDDR4 has no relationship to DDR4.