In English, "to feel lonely" means "to feel sad about not having a sole mate around", whereas "to be alone" means "not to have anobody around". I have never heard people say "he felt alone", only " he felt/was feeling lonely", so I doubt that the translation offered by DL as correct is indeed correct. I tend to think it is a mistake. If you confirm it, I'll report it.
The clitic "si" ("himself") indicates this a reflexive use of the verb sentire, which always indicates feeling about oneself (feeling well, sick, alone, etc).
Lui sente solo = He heard alone (assuming for a second that's a sensible sentence)
Lui si sente solo = He felt alone