What you are describing suggests a link issue. Perhaps replacing the ethernet cable between the Fritz and the Asus might resolve your issue. Other possibility is that your Asus was also fried as a result of the lightning strike
Unlikely, IMO, this is a problem of using the Asus as a router.
There is no reason to believe that using the Asus as router is a problem, yes there is a double-NAT unless he has the firewall turned off, but he has it as Auto-IP from the Fb, so IMO an intermittent performance issue suggests cabling or hardware failure.
I have a similar setup, although I have my Asus in front handling the PPPoE and the Fb behind handling 'routing' and telephony (SIP via AAISP), I've had many a router over 2 decades and a lightning strike can easily affect multiple devices, some may have more apparent faults than others. OP indicated the original Fb was fried, so collateral damage to other equipment cannot be ruled out.
Edited by wiggsc00 (Wed 25-Sep-24 17:40:40)