Hi Zhaozhang,
1. No, this is not supported by LPUART. There's a note in section "76.1.1 LPUART instances and configuration":
"LPUART instances are not available during Standby."
2. FlexCAN itself is also not in Standby Power Domain, so you can't use the FlexCAN module directly to wake up the chip.
However, there's a workaround. See the Wakeup Unit section in the reference manual. WKPU supports 4 internal sources and 60 external sources that can generate interrupts or wakeup events.
It also supports a non-maskable interrupt input.
The wakeup sources are:
WKPU0 : SWT0 wakeup, RTC API wakeup.
WKPU1 : RTC timeout.
WKPU2 : Round robin interrupt from any of the three comparators.
WKPU3 : RTI wakeup
WKPU4 - WKPU63 : External pin wakeup sources
The external pins can be used for this purpose. LPUART_RX pins or CAN_RX pins share the function with WKPU. So, even if LPUART or FlexCAN are in low power mode, these pins can be still configured in WKPU to wake up the chip on rising or falling edge.
Regards
Lukas