Conversation so far:
How did T. E. Lawrence get interested in antiquities and archaeology?
At age 15, T. E. Lawrence and schoolfriend Cyril Beeson cycled around Berkshire, Buckinghamshire, and Oxfordshire, visiting almost every village's parish church, studying their monuments and antiquities, and making rubbings.
Did T. E. Lawrence attend school?
T. E. Lawrence attended the City of Oxford High School for Boys from 1896 until 1907, where one of the four houses was later named Lawrence in his honour.
What did T. E. Lawrence and Cyril Beeson do at the sites?
The Ashmolean's Annual Report for 1906 said that the two teenage boys, T. E. Lawrence and Cyril Beeson, by incessant watchfulness secured everything of antiquarian value which has been found.“
Did T. E. Lawrence and Cyril Beeson travel anywhere else?
In the summers of 1906 and 1907, T. E. Lawrence and Cyril Beeson toured France by bicycle, collecting photographs, drawings, and measurements of medieval castles.
What is an interesting fact about T. E. Lawrence's early travels besides touring France by bicycle?
In summer of 1909, T. E. Lawrence set out alone on a three-month walking tour of crusader castles in Ottoman Syria
What did T. E. Lawrence accomplish while in Syria in the summer of 1909?
In summer of 1909, T. E. Lawrence set out alone on a three-month walking tour of crusader castles in Ottoman Syria, during which he travelled 1,000 mi on foot.
What archaeology did T. E. Lawrence participate in after 1909?
In 1910, T. E. Lawrence was offered opportunity to become a practising archaeologist at Carchemish, in the expedition that D. G. Hogarth was setting up on the British Museum's behalf.

Question: who was he working for?
Self-contained rewrite: who was T. E. Lawrence working for in the expedition that D. G. Hogarth was setting up on the British Museum's behalf in 1910?