Lonesome is already a very strong word expressing a high degree of solitude and sadness. To express a greater degree of these feelings, you would use intensifiers or other descriptive words, like:
* More lonesome
* Extremely lonesome
* Utterly lonesome
* Desperately lonesome
* Most lonesome (this is often used in poetic or figurative language)
Remember, the most effective way to convey a heightened sense of loneliness is through the use of strong imagery and vivid descriptions.