Piccadilly is right by Terminal 2, whereas HEX/EL is fairly close to T3, hence HEL/EL is indeed the answer to that question. For some time now all 3 services have had various outages, so on the day check the relevant websites/apps for any disruption updates, since if HEL / EL has big service gaps then it may well be worth taking the underground travelators to get to T2 / Piccadilly on foot. They all use contactless for the free ticket, HEX dispenses free transfer tickets from a clearly marked set of machines if you don't have a contactless card or device. For completeness, if all rail based systems are not working - a rare event - then there are bus service options too from the Central Bus Station above the Piccadilly line station at T2.