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Despite various advances in automatic speech recognition (ASR) technology, recognition of speech uttered by non-native speakers is still a challenging problem. In this paper, we investigate the role of different factors such as type of lexical model and choice of acoustic units in recognition of speech uttered by non-native speakers. More precisely, we investigate the influence of the probabilistic lexical model in the framework of Kullback-Leibler divergence based hidden Markov model (KL-HMM) approach in handling pronunciation variabilities by comparing it against hybrid HMM/artificial neural network (ANN) approach where the lexical model is deterministic. Moreover, we study the effect of acoustic units (being context-independent or clustered context-dependent phones) on ASR performance in both KL-HMM and hybrid HMM/ANN frameworks. Our experimental studies on French part of MediaParl as a bilingual corpus indicate that the probabilistic lexical modeling approach in the KL-HMM framework can capture the pronunciation variations present in non-native speech effectively. More precisely, the experimental results show that the KL-HMM system using context-dependent acoustic units and trained solely on native speech data can lead to better ASR performance than adaptation techniques such as maximum likelihood linear regression.