Is there something like iRule instance ID that could be printed easily on the ltm log?

This is application specific and recommend identifying something on the application side that is used for session identification as even if some iRule session ID is available it would only be for the single execution of the the set of iRules.

For example if you have a Web App that uses JSESSIONID cookies/headers then I would log using that bit of info.

It is hard on the F5 side as you can identify a TCP or SSL connection/session with easy but that only works if you have a single TCP connection for each application session. For example HTTP this would not work as you could have many connections over the course of a users sessions or something like a proxy upstream doing HTTP multiplexing.

If this helps please up vote my answer/comment.