Having just re-read Lynch's paper, can you explain what you mean here? I didn't see anything explicitly relying on time. It could be there is some implicit usage I didnt see. Additionally, the paper's impossibility result is about "perfectly correct consensus" which applies with and without clocks and then has a positive result for "partially correct consensus" (i.e. not deciding a value is a correct result). Im not sure which you mean when you say "consensus becomes impossible" as it is either already impossible (the perfectly correct protocol) with one faulty process or (to my understanding) not dependent on time (the partially correct protocol).
p.s. great article!