No. Minitab is not necessary for improvement projects, especially in a Lean initiative.
There are many projects that do not use any form of statistical software. Minitab is a statistical software that is mostly suited for applying statistical tools in the Six Sigma DMAIC methodology.
For example, if someone wanted to use statistical tests such as ANOVA, Regression, T-Tests, or F-Tests, to name a few, Minitab can be used. In addition, Minitab also has graphical tools such as box plots, histograms and pareto charts that can be easily run in this software. It is a popular choice for statistical software because Motorola, GE and other large organizations that have implemented a Six Sigma initiative have chosen this statistical software.