finding the LTM based on the VIP

 , well if your on the internal network, you should be able to simply login to some server and run a tracepath to that VIP. That will give you back the last hop of that VIP, which will be the self IP of the LTM.

With Self IP also you can login to the LTM. So job done 🙂

#tracepath 1.1.1.1

-sh-4.2$ tracepath 1.1.1.1
 1?: [LOCALHOST]                                         pmtu 1500
 1:  xyz   0.209ms
 1:  xyz   0.146ms
 2:  abc   0.220ms
 3:  def   0.638ms
 4:  xyz   2.388ms
 5:  qwe   44.891ms
 6:  fqdn-name.company.com                             0.306ms
 7:  no reply
 7:  ltm-hostname-vs.company.com               6000.075ms !H
     Resume: pmtu 1500
-sh-4.2$

Let me know how it goes.