I’ve read the specs and it seems they’ve implemented some kind of low power mode in AT slave firmware. Key point to me is RX pin (looking from LoRa-E5 side) should not change during sleep, ie it should not be floating. They do not say anything about 9600, so it does not seem to be LPUART. Probably they just switching between using RX pin for UART (wake-up mode) and GPIO external interrupt in sleep? May be look via scope what is happening on RX pin when you send AT+LOWPOWER=AUTOON?
5mA seems like radio is always on. Did you switched to Class A device? What other devices are connected to your board? Any LED is on maybe? or a sensor. Even connected debugger probe sucks some current, but not 5mA