You won't get to talk to ElderL yons until further on into the main quest.

Sorry forgot He's in the Citadel

Elder Lyons is in the Citadel which is in the south-eastern part of the map. If you go south from the Supa-Dupa Mart you should be able to find it

You meet him after the main quest:The Waters OfLlife once you get through the tunnels with all the Enclave soldiers when you enter the citadle with Doctor Li.

Keep doing the main story line and you will get to him at the Citadel.

To get into the Citadel you keep doing the main story line, about half way in it.

When you find your dad and you go the Rivet City to talk to Doctor Li they will go to the Purity place (sorry forget name) and they'll tell you to do some stuff there like clear it out and other basic stuff. After awhile doing this and when you go to the sewer tunnel (don't worry it says to and easy to find) the Enclave comes and someone dies. After awhile you leave with Doctor Li and other people and you end up at the Citadel and they let you in and you can meet the guy.

Might seem long but it isn't really so don't worry

Elder Lyons is located at the Citadel.