Being alone, as bramble shows, does not mean you are lonely. You can be lonely in a relationship or when surrounded by people.
We do reach out to friends, who are alone and one friend comes along most Christmases for an hour or so in the afternoon. I tentively asked another friend to spend Christmas with us, as she has recently been bereaved and has little family. I am aware that being around others may be harder than being alone. Her great niece has invited her, but it meant a lot to her that I asked her. This Christmas will be a difficult time for her.