The tree mentioned above shows that she was also known as Lucy Johnson and that William was known as James Cook which accounts for why there is no marriage for a Louisa Ada Johnson to a William J Cook on freebmd
The tree also says she died in January 1907 in Wimbledon and the only death in the March qtr 1907 is a Lucy Louisa Cook aged 35
Here's the 1901 entry for Wimbledon - all children born there
James Cook 37 b Basingstoke - navvy
Louisa A 27 b Battersea
James W 7
Florence R 4
Minnie A 2
George A 4mths died December qtr 1902
Eleanor G 4mths
RG13 Piece 660 Folio 27 Page 45