What is the best way to verify new IP address is not used on F5 ltm

This will show you all self-IPs, float IPs, and all VS IPs:

( tmsh list /ltm virtual one-line ; tmsh list /net self one-line ) | egrep '^(ltm virtual|net self) ' | sed -e 's/^.* destination //g' -e 's/^net self //g' | cut -d' ' -f1 | cut -d: -f1 | sort -t. -n -k1,1 -k2,2 -k3,3 -k4,4 | uniq

You need to run it on F5

Or, remotely via SSH:

ssh YOUR-BIG-IP "( tmsh list /ltm virtual one-line ; tmsh list /net self one-line )" | egrep '^(ltm virtual|net self) ' | sed -e 's/^.* destination //g' -e 's/^net self //g' | cut -d' ' -f1 | cut -d: -f1 | sort -t. -n -k1,1 -k2,2 -k3,3 -k4,4 | uniq

Or, if you don't have a full shell, but tmsh cli only:

ssh YOUR-BIG-IP "list /ltm virtual one-line ; list /net self one-line" | egrep '^(ltm virtual|net self) ' | sed -e 's/^.* destination //g' -e 's/^net self //g' | cut -d' ' -f1 | cut -d: -f1 | sort -t. -n -k1,1 -k2,2 -k3,3 -k4,4 | uniq

I have written a wrapper script for it, which shows me all used and free F5 IPs in a specific subnet. I might just share it somewhere.