Umpires may certainly consult each other and do maintain separate jurisdictions. The newest version of the Laws of Cricket, dated 1st October 2017, published by the MCC, has several clauses dealing with this (they haven't changed significantly in meaning since the last version):
2.11 Disagreement and dispute
Where there is disagreement or dispute about any matter, the umpires together shall make the final decision. See also Law 31.6 (Consultation by umpires).
31.6 Consultation by umpires
Each umpire shall answer appeals on matters within his/her own jurisdiction. If an umpire is doubtful about any point that the other umpire may have been in a better position to see, he/she shall consult the latter on this point of fact and shall then give the decision. If, after consultation, there is still doubt remaining, the decision shall be Not out.
Unfortunately the Laws themselves are somewhat less explicit about which umpire has jurisdiction for each decision, only sometimes explicitly assigning them to the bowler's end umpire or not. In my experience of the game, the bowler's end umpire would certainly consider an LBW appeal his or her job and give the final decision, but only a foolish umpire in a bad umpiring team wouldn't listen to information from his/her colleague if they had anything to say.