Why there were changes in molar mass of lithium?
This doesn't necessarily completely answer the question, but it at least moves closer to the root of the problem. From the Wikipedia article that MaxW included in his comment: 


  Brande also described some pure salts of lithium, such as the chloride, and, estimating that lithia (lithium oxide) contained about 55% metal, estimated the atomic weight of lithium to be around 9.8 g/mol (modern value ~6.94 g/mol)


So it seems to stem from an erroneous estimation of the percent composition of lithium oxide. If we go to the source (Brande's manual of chemistry:https://books.google.com/books/reader?id=zkIAAAAAYAAJ&amp;printsec=frontcover&amp;output=reader&amp;pg=GBS.PA190), we find that this error likely stems from the fact that lithium oxide was difficult to obtain and so very limited experimentation had been done to characterize it.