This may not be what you want to hear, but oftentimes you are better off trying to create the entire LP/IP in MPS format from scratch. You might actually end up saving time over converting from Lingo.
If you do want to convert, I suggest that you first load a much smaller problem onto LINGO and see if you are able to convert that first. Then incrementally keep increasing the size of your LP to see where you are getting the errors. This document has instructions on converting an existing problem to the MPS format.
In addition to LPSolve, you might want to try other open-source/free solvers. Some of the common ones include GLPK, SCIP, Google-OR Tools. If you know R, then optim
and several other options are available. Finally, I've found that Excel's Solver is quite good as well.
Hope this helps you move forward.