thank you for your reply message on the Kentucky Genealogy Forum.
Yes, it seems to answer my question. Kate and Lila are sisters. That will mean that their parents were: "M. B. Morrison and Kate Taylor".
BTW. Robert J. Breckinridge and Kate Morison did indeed have (as far as I know) two children:
1) Robert J. (born June 1, 1859 , died Oct 12, 1899) 2) Morrison (born 1873, died April 11, 1912, age 38)
As far as I know Robert and Lilla Morrison had no children.
Robert, Kate and Lilla are all buried at Lexington Cemetery (Lot 134, Section O). Robert in the middle, left Kate, right Lilla. On short distance (just behind the graves of Robert, Kate and Lilla) are 3 graves, i.e. the graves of Morrison and her brother Robert J. and Mrs Douglas W. Breckinridge (passed away, Oct 5, 1953, age 80, so born in 1873). Don't know how she is related.