In block lattice with DPoS consensus, there is no PoW miners competition, and each client account maintains its own blockchain. Therefore, there is only one reason for a fork - when the fork is created by the account owner, intentionally (trying to "double-spend") or occasionally (software error). In this case, the network simply retains the transaction (block) that receives the supermajority (⅔+1) of approvals from the authorizers. The (legitimate) authorizer cannot authorize two transactions pointing to the same previous block, so one of those transactions will be always rejected. Note that if the blocks are created simultaneously, there is no guarantee which transaction will be authorized first.