One of the key challenges involved in building statistical automatic speech recognition (ASR) systems is modeling the relationship between subword units or “lexical units” and acoustic feature observations. To model this relationship two types of resources are needed, namely, acoustic resources i.e., speech data with word level transcriptions and lexical resources where each word is transcribed in terms of subword units. Standard ASR systems typically use phonemes or phones as subword units. However, not all languages have well developed acoustic and phonetic lexical resources. In this paper, we show that the relationship between lexical units and acoustic features can be factored into two parts through a latent variable, namely, an acoustic model and a lexical model. In the acoustic model the relationship between latent variables and acoustic features is modeled, while in the lexical model a probabilistic relationship between latent variables and lexical units is modeled. We elucidate that in standard hidden Markov model based ASR systems, the relationship between lexical units and latent variables is one-to-one and the lexical model is deterministic. Through a literature survey we show that this deterministic lexical modeling imposes the need for well developed acoustic and lexical resources from the target language or domain to build an ASR system. We then propose an approach that addresses both acoustic and phonetic lexical resource constraints in ASR system development. In the proposed approach, latent variables are multilingual phones and lexical units are graphemes of the target language or domain. We show that the acoustic model can be trained on domain-independent or language-independent resources and the lexical model that models a probabilistic relationship between graphemes and multilingual phones can be trained on a relatively small amount of transcribed speech data from the target domain or language. The potential and the efficacy of the proposed approach is demonstrated through experiments and comparisons with other approaches on three different ASR tasks: non-native and accented speech recognition, rapid development of an ASR system for a new language, and development of an ASR system for a minority language.