If im not mistaken, it was mentioned that the BL's that rise are those with emotional ties the the different type of corp members. Lar has ties not only to those he killed to become AO, but to the other lanterns hes killed, thus being risen by the BLC. Now, why hed no longer be able to make constructs is beyond me. IF, and i say IF that the case, im calling bs on that one.
As a lantern, he should be able to make constructs whether its of former allies or other corps members and have them not be turned. For example, when Arisa's family were BL's she also made constructs of her family(if im not mistaken) and escaped.