When we say that Some people have lungs, we implicate that not all people have lungs. This scalar implicature arises when we produce a weaker expression instead of a stronger one. Studies on bilingual adults suggest that L2 learners, regardless of their proficiency level, are sensitive to under-informative sentences and they exhibit a superior pragmatic ability on a par with monolingual control groups. However, the evidence obtained from these studies is largely one-dimensional stemming from offline tasks that provide limited information about scalar implicature processing. The present study addressed this issue by investigating scalar implicature computation among L2 adults using an online sentence verification paradigm similar to that of Bott and Noveck whereby participants are required to judge the veracity of categorical under-informative sentences. The study also examined how individual differences in personality traits and L2 proficiency level would modulate participants’ pragmatic responses and processing times. Our results showed that those with weaker English proficiency tended to be significantly less sensitive to implicatures than those with proficiency advantage. The two proficiency groups also took significantly longer processing times to compute the pragmatic interpretation than the logical interpretation. The results further revealed that the pragmatic responses and their processing slowdowns were influenced by various personality and autistic traits. Our findings provide novel empirical insights into how L2 learners process scalar implicatures, and thus useful implications for the processing theories in experimental pragmatics and second language acquisition.