English. Latinate feminine form of Louis, from Old German "famous warrior", in use as an English forename since the 18th century.
A number of spelling variations occur in the 1841 Census of Aberdeenshire for Louisa and Louise. These include Lousia, Louiza, Lousa, Lowesa and Loues. When searching old records, these spellings should be considered as possible variants. Most, if not all, should be returned by a Soundex search.
A correspondent [MJB] has recorded a possible use of Louisa as a short form or pet name for Elizabeth. This may be a local spelling variant of Liza but we have no evidence to support this.