How to Get IP address from MAC Address using ESP8266 wifi Module
Use the inverse ARP protocol.  See http://en.wikipedia.org/wiki/Address_Resolution_Protocol#Inverse_ARP_and_Reverse_ARP .  I don't know if the module you are using can do this, or if you will have to do this yourself.  The basic idea is to send an Ethernet packet to the MAC address in question with the 8 in the OPER field.  The device at the other end should respond with the IP address filled in properly and 9 in the OPER field.  Also see http://www.networksorcery.com/enp/rfc/rfc2390.txt .  This does rely on the device at the other end supporting InARP.  If it doesn't, I'm not sure if there is much of anything you can do about it.  Another thing you could try is broadcasting ARP requests for each IP in the subnet and hope that you get the response you want.