I thought at first it might be the SMLE variant for completing the final War Story, but that's not the case. Then I thought it might be a super rare Supply Crate unlock. Not that either. Queue the Google search!
According to this thread from Battlefield's forum, the Lawrence of Arabia SMLE is a Deluxe Edition addition. You can get it by upgrading your game to the Deluxe Edition, but that will set you back around $20.
Buying the Premium Pass for the game only gets you access to all DLC for the game, not the special bonuses for higher tiers of the game (Deluxe or Ultimate).