The 19-year-old striker who made his first team debut as a substitute against Wigan last month looked sharp and bagged his treble before departing on the hour.
Massimo Luongo, a driving force in central midfield, was also on the scoresheet alongside Will Ekong, Simon Dawkins and Cristian Ceballos.
Brazilian Under-20 international Bruno Uvini, on trial at the club for two months, played for an hour at centre-back and there was a return from long-term injury for young defender Nathan Byrne, who played the full 90 minutes.
Lancaster opened the scoring in the sixth minute, firing home low at the near post from 16 yards.
The Os gave as good as they got in a competitive first half and soon levelled when Moses Odubajo squared for experienced striker Jamie Cureton to tap home.
Alex Pritchard hit the post before Luongo provided a cool finish one-on-one from Lancaster's pass for 2-1 in the 27th minute.
Orient hit back again through David Mooney and Jonathan Miles was forced to make saves from Mooney and Cureton before Pritchard struck the woodwork again, this time his free-kick clipped the top of the crossbar.
Lancaster headed us into the lead from Pritchard's corner five minutes into the second half and completed his hat-trick seven minutes later, rolling home Byrne's cross after the full-back's run from deep caught the Os defence square.
Tim Sherwood made three changes on the hour with Souleymane Coulibaly, Ekong and Giancarlo Gallifuoco on for Lancaster, Uvini and Pritchard and it took just four minutes for Ekong to make his mark, a fine diving header from Luongo's cross for 5-2.
Miles made three more fine saves before a flurry of late goals.
Byrne crossed deep for Ceballos to head home for 6-2, Dawkins slid home after good work from Coulibaly and Luongo for 7-2 in the last minute but Orient had the final word when Billy Lobjoit made it 7-3 in added time.
Spurs XI: Miles; Waller Lassen, Khumalo, Uvini (Ekong, 60), Byrne; Ceballos, Luongo, Veljkovic, Pritchard (Gallifuoco, 60); Dawkins, Lancaster (Coulibaly, 60).
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