I certainly haven't seen any original records, so you may be right that
Alivia is a typo for
Alicia. On the other hand, if it's a mistake, then it's a mistake that many people have made. Google "
Alivia Braose" or "
Alivia de Braose" and you'll find numerous geneological pages that reference her. Curiously, some of these websites also call her
Aline, a name which is supposed to be related to
Adeline, not
Alice.
I looked for some more medieval Alivias and came across two more: both of them named
Alivia Bassett, both living in the 13th century. The second
Alivia Bassett is *also* called
Aline in some sources. She was the mother of a famous English lord named
Hugh le Despenser the
Elder, and is referred to as
Alivia by more than one source. So I suppose
Alivia is somehow related to either
Alice or
Aline.
BTW, all my "research" comes from the internet, so there's always the possibility that there are some of the websites I've seen aren't too reliable. :)