Does for redundant LTM devices need to be configured with HA with gateway and vlan fail-safe mode to avoid service disruption?

Sounds like you're using aggregated links / trunks from your description. If so then I'd recommend HA Group to monitor the health of the interfaces within this trunk. i.e. if an interface goes down then possibly failover.

I believe this is recommended over vlan fail-safe as it's quicker to failover (it's called Fast Failover). But for extra redundancy then vlan fail-safe is an option. Basically it checks that traffic is traversing this vlan (on a per vlan basis) and if not then it will initiate traffic before deeming that there is an issue (interface down) and failing over.

Hope this helps,

N