Previous studies have demonstrated that male European lobsters (Homarus gammarus) use chemical and visual signals as a means of intraspecific communication during agonistic encounters. In this study, we show that they also produce buzzing sounds during these encounters. This result was missed in earlier studies because low-frequency buzzing sounds are highly attenuated in tanks, and are thus difficult to detect with hydrophones. To address this issue, we designed a behavioural tank experiment using hydrophones, with accelerometers placed on the lobsters to directly detect their carapace vibrations (i.e. the sources of the buzzing sounds). While we found that both dominant and submissive individuals produced carapace vibrations during every agonistic encounter, very few of the associated buzzing sounds (15%) were recorded by the hydrophones. This difference is explained by their high attenuation in tanks. We then used the method of algorithmic complexity to analyse the carapace vibration sequences as call-and-response signals between dominant and submissive individuals. Even though some intriguing patterns appeared for closely size-matched pairs (<5 mm carapace length difference), the results of the analysis did not permit us to infer that the processes underlying these sequences could be differentiated from random ones. Thus, such results prevented any conclusions about acoustic communication. This concurs with both the high attenuation of the buzzing sounds during the experiments and the poor understanding of acoustic perception by lobsters. New approaches that circumvent tank acoustic issues are now required to validate the existence of acoustic communication in lobsters.