@jun1
I've been waiting to see if anybody else has replied to this as I have had this requirement in the past and never found a foolproof way of resolving the issue.
When I look at the RM for LVD (bit 1) of SIM_SRSID the RM Register/Bit description says pretty definitely that "This field is also set by POR." which means that it won't work the way you want it.
However, might I suggest that you look at the LVWACK in the PMC_SPMSC1 register - according to the RM it comes up as 0 on POR and is set when an LVD has happened. You would need to try this to see if it works as it seems to be described.
Regardless, determining when an MCU is coming out of reset due to a POR or LVD event can be non-trivial. The best way I found to handle the situation (on another device) was to monitor the Vdd level with a comparator pin (in my case using a Zener as the reference) and when Vdd dipped below what I considered acceptable but above the MCU's trip point then I handled it as an LVD event and ignored the internal "LVD"/"POR" bits in the MCU's registers all together.
The other approach I've used (and had to convince the customer of) is to treat all resets as POR events and reset the whole system - which isn't a bad assumption becaue if Vdd has dropped to the point where the MCU resets then everything running in the system is at a suspect state.
Good luck, let me know how it works out for you,
myke