The adverb is "lonelily", but people rarely use it.

Hali is completely correct. "Lonelily" is a perfectly good word. I'm flabbergasted. I would never have believed it. I'm a college-educated U.S. native speaker and I have NEVER seen or heard this word. I would have bet money that it does not exist. But I checked a dictionary and it is there. And there are examples of its use in Project Gutenberg, for example: "Educated at a provincial academy, he had been removed at the age of sixteen to Rochebriant, and lived there simply and lonelily enough, but still in a sort of feudal state, with an aunt, an elder and unmarried sister to his father."--Edward Bulwer-Lytton "they say, he used to sit for hours, wrapt up in thought,--brooding lonelily over the first stirrings of passion and genius in his soul..." --Life of Lord Byron, Thomas Moore If I saw it in print, I would know what it meant. I don't think I'd ever use it myself. I don't even know what it means to do something lonelily--either you ARE alone or lonely or you are not, it's not a characteristic of an action. If I had to express the idea itself, I would either use the phrase "in a lonely way."

The short answer is I do not think so. I don't recall ever using 'lonely' as an adverb, and I can't find anything on the internet to counter this. That said, to answer your question, I have to ask a question. Are you trying to describe the street as lonely, or the person walking along the street is lonely? In English (and probably other languages too), we can convey a mood by also describing the scene. With the first, "He wandered around the lonely streets." This means that the streets were fairly empty, but does not necessarily speak to the state of the subject's loneliness. It can be inferred that the subject is lonely because he or she is wandering the streets alone, but you would need more narration to fully convey this. With the second, "He walked lonesomely around the streets," it is understood that the subject is lonely. 'Lonesomely' is specifically describing how the subject was walking and also conveys the mood. I think that you are perhaps looking for the second option. Hope this helps.

Perhaps "solitarily" is the right word.