Mobile applications are becoming complex software systems as they rapidly evolve and grow constantly to meet user requirements. However, satisfying these requirements may lead to poor design choices known as 'antipatterns' that can degrade software quality and performance. Therefore, perception and monitoring of the characteristics of mobile applications are important activities to facilitate maintenance and development, so that developers are directed to restructure their practices and upgrade their qualifications. This study aims to better understand the development of complexity, size and internal quality in the evolution of mobile applications and, in particular, to investigate the validity of three of Lehman's laws (increasing complexity, continuous growth, decreasing quality) in mobile applications. In this context, an exploratory study was carried out by analyzing the evolution of application quality, according to hypotheses established and using object-oriented design metrics in 61 versions of three Android-based mobile applications. As a result of the analyses, Lehman's 'continuous growth' law was validated for all apps, while the 'increased complexity' and 'declining quality' laws have not been validated. In addition, the results of the experimental study have been verified with Spearman correlation analysis and it was observed that there is a significant relation between the design metrics and the quality attributes.