Need steps to reboot Big IP LTM in HA pair without impacting production?

I am assuming you want to reboot in order to upgrade code - is this right ?

Normally, this sequence would be of help:

1. Reboot secondary
2. Failover from active to secondary.
3. Reboot current secondary.
4. If need be, you can fail back to the original active device (current standby).

It is important to know that the sequence of reboot/failover events will minimise the downtime but not completely remove it. You should perform the steps under a maintenance window and prepare for downtime of about 1 minute when failing between the devices. The actual duration could be higher depending on features like persistence, mirroring and the robustness of your application to recover from packet loss that will occur during failover.