In a normal stable network a DHCP lease never actually expires, instead it regularly extended. This is done by the DHCP device checking with the DHCP server appropiamately half-way through the lease whether its okay to continue with that address at which stage the lease is reset.
What you describe might implies some fault in the network, a DHCP server or IP address address conflict most likely which is causing the phone to ask for a new address and reset. Given its only affecting one person I would start by being suspicious of their other equipment (PC, mobile, printer, etc).
However, it may just be your phrasing, but to quote "At the exact time it power cycled itself the DHCP lease was renewed on the server, and the last date and time of license allocated for that phone in Avaya was renewed" - that's absolutely normal operation. When any IP phone power cycles it will renew its lease and license. So you may be interpreting the DHCP/license renewals as a problem/problem cause when they are not, it might just be a dodgy power cord or the CEO keeps flipping the wrong power switch when plugging in his PC.
Stuck in a never ending cycle of file copying.