Back in September 2018, the Texas Bar Ethics Committee issued a short ethics opinion trying to explain the proper analysis attorneys should follow to determine if they owe a duty to a third party who claims to have an interest in client money in the lawyer's trust account.
More specifically, the opinion addresses these two questions: "when does a third party have an interest in client funds sufficient to trigger a lawyer’s duty to disburse or safeguard those funds for the third party’s benefit?" and "[d]oes termination of the attorney-client relationship affect a lawyer’s duty to safeguard or disburse client funds in which a third party claims an interest?"
You can read the opinion online here or download it in pdf here.
UPDATE (7/1/19): Ethical Grounds has posted a comment on the opinion here.