This paper focuses on the development of tools for analyzing the stochastic gravitational wave background (SGWB) from inflation using the Laser Interferometer Space Antenna (LISA). The authors introduce a template-based approach to describe and reconstruct well-motivated inflationary signals, aiming to enhance the sensitivity of LISA to these signals. They classify seven templates based on their frequency shape and identify fundamental physics models that generate them. The templates include power-law, log-normal bump, broken power law, double peak, excited states, linear oscillations, and logarithmic resonant oscillations. The paper details the construction of the SGWBinner pipeline for template-based searches and parameter estimation. It forecasts the accuracy of LISA in reconstructing these templates, both with and without foregrounds, and discusses how these reconstructions can provide insights into inflationary models. The study highlights the potential of LISA to probe inflationary parameter spaces and the impact on measurements of axion couplings, graviton mass, primordial black hole seeds, and small-scale spectral features.This paper focuses on the development of tools for analyzing the stochastic gravitational wave background (SGWB) from inflation using the Laser Interferometer Space Antenna (LISA). The authors introduce a template-based approach to describe and reconstruct well-motivated inflationary signals, aiming to enhance the sensitivity of LISA to these signals. They classify seven templates based on their frequency shape and identify fundamental physics models that generate them. The templates include power-law, log-normal bump, broken power law, double peak, excited states, linear oscillations, and logarithmic resonant oscillations. The paper details the construction of the SGWBinner pipeline for template-based searches and parameter estimation. It forecasts the accuracy of LISA in reconstructing these templates, both with and without foregrounds, and discusses how these reconstructions can provide insights into inflationary models. The study highlights the potential of LISA to probe inflationary parameter spaces and the impact on measurements of axion couplings, graviton mass, primordial black hole seeds, and small-scale spectral features.