I don't think so. I have no idea how one would write "a lonely letter" in French. "Lettre de solitude"? Maybe "une lettre seule"? (whereas I would assume that "une lettre toute seule" would translate to "The woman writes a letter all by herself") Hopefully a native speaker chimes in on this one because I'm curious how one would write it.
I think we have to realize that one doesn't say things the same way in French as one says them in English. Every new speaker of English runs into this as well, in reverse. The French probably would not say that one writes a lonely letter. Maybe they would say that 'she writes a letter expressing her loneliness' or some such thing. Just thinking here.
She writes a single letter. She writes a sole letter. She writes one letter only. These are all equivalent and I would use any of them. She writes only one letter works too, but could be ambiguous. She writes only one letter (but three novels), for example. In other words, it could suggest that a letter is not all she writes. Something to do with the placement of only. Anybody else help here?