Lateral flow assays and paper microfluidics have the potential to replace benchtop instrumented medical diagnostic systems with instrument-free systems that rely on passive transport of liquid through micro-porous paper substrates. Predicting the imbibition dynamics of liquid through dry paper substrates is mostly modeled through the Lucas-Washburn (LW) equations. However, the LW framework assumes that the fluid front exhibits a sharp boundary between the dry and wet phases across the liquid imbibition interface. Additionally, the relative humidity in the environment results in moisture trapped within the pores of the paper substrates as the paper attains an equilibrium with the ambient air. Here, we apply a two-phase transport framework based on Brooks and Corey's model to capture imbibition dynamics on partially saturated paper substrates. The model is experimentally validated and is then used to predict the liquid-paper imbibition dynamics in simulated environments with 1-70% relative humidity. The model was also used to determine the saturation gradient of liquid along the imbibition interface of the paper substrate. Insights from these studies enabled us to determine the mechanism of the liquid transport in partially saturated porous paper substrates. The model also enabled us to evaluate the optimal paper shapes and relative humidity of the environment that maximize imbibition rates and minimize imbibition front broadening. Finally, we evaluate the effect of moisture content of paper on the rate of paper-based biochemical reaction by amplifying a sequence of the SARS-CoV-2 RNA target via reverse transcriptase loop-mediated isothermal amplification. Taken together, this study provides some important guidelines to academic and applied researchers working in point-of-care diagnostics to develop paper-based testing platforms that are capable of functioning in a robust manner across multiple environmental conditions.