If you happen to see him, please tell him to call me.
Literal
By-chance him [to-に] meet-[conditional-たら], me [to-に] telephone [object-を] do [purpose-ように] say-[polite request-てください].
ように here functions as the indirect-command frame: [verb-plain form] + ように言う ('tell someone to X'). It's how Japanese reports a command or request. に marks both the met person (彼に会う) and the recipient of the relaying (私に言う).