Standard hidden Markov model (HMM) based automatic speech recognition (ASR) systems use phonemes as subword units. Thus, development of ASR system for a new language or domain depends upon the availability of a phoneme lexicon in the target language. In this paper, we introduce the notion of probabilistic lexical modeling and present an ASR approach where a) first, the relationship between acoustics and phonemes is learned on available acoustic and lexical resources (not necessarily from the target language or domain), and then b) probabilistic grapheme-to-phoneme relationship is learned using the acoustic data of targeted language or domain. The resulting system is a grapheme-based ASR system. This brings in two potential advantages. First, development of lexicon for target language or domain becomes easy i.e., creation of a grapheme lexicon where each word is transcribed by its orthography. Second, the ASR system can exploit both acoustic and lexical resources of multiple languages and domains. We evaluate and show the potential of the proposed approach through a) an in-domain study, where acoustic and lexical resources of target language or domain are used to build an ASR system, b) a monolingual cross-domain study, where acoustic and lexical resources of another domain are used to build an ASR system for a new domain, and c) a multilingual cross-domain study, where acoustic and lexical resources of multiple languages are used to build multi-accent non-native speech recognition system