The answer is Yes and No, but mostly No. The APQ8016 processor IC does support LPDDR2, you can see this by reading the device specification available at https://www.96boards.org/products/ce/dragonboard410c/documentation/.
However you will find that the 410c board uses a eMCP part from Sandisk (full part number is on the Bill of Materials also on the documentation page). As a bit of background for other readers of this post, an eMCP part is an "embedded Multi-Chip-Package" containing both eMMC storage and LPDDR3 DRAM. The 410c PCB is laid out for the eMCP part, and you will not be able to substitute a pure LPDDR2 part onto the board.
The next issue is the DRAM controller in the APQ8016 must be initialized up to control LPDDR2 memory, and the default initialization code does not do this. The DRAM controller initialization code runs long before LK starts and access to initialization source code is not generally available.
If you need a board that has a specific LPDDR2 part on it, you will need to work with one of the Companies that design and build boards based on the APQ8016 (examples, Intrynsic, InForce Computing, and eInfoChips). They will be able to modify the bootloader and build a board with LPDDR2 for you. This work will likely incur significant cost to you.
Finally only a few LPDDR2 eMCP parts have been qualified, you will need to use a qualified part, not all LPDDR2 parts have been tested.
I am curious as to 'why' you would want to change to LPDDR2 memory on the 410c board?
Full Disclosure: I am an employee of Qualcomm Canada, any opinions I may have expressed may not reflect the opinions of my employer.