I am learning about linear optimization in R using the lpSolve package. I am wondering if the lp() function in R can sometimes find a solution that is a saddle point and not the true min/max. I have looked at the documentation of the package and I haven't found anything about saddle points or how the optimization function works. Do you know if this is possible?
No. LP solvers find the global optimum. Saddle points or local optima are not an issue.