Can't help for definite but putting possible scenarios in (please don't take offence at the suggestions)
On the 1891 census Walter & Jane's 2 other sons are 14 and 13, by 1901 is it possible that one of them, Walter jnr ?, has fathered a child (with Miss Talbot) who is living with Jane, I think a 20 year age gap between Walter jnr, Lionel and Frederick is not biologically impossible but unlikely (by 1901 Jane was 51, a bit late in life for another child)
The other possible scenario is that Walter Snr is his father but he has a different mother and Jane is looking after him. Maybe Leicester was where he was in 1901 but he could have been anywhere in the country before then. In later life 'Fred' took the Butler surname.
Have you got actual copies of the workhouse and orphanage records? I can't get into the London Metropolitan Archives online catalogue today to check out their holdings.
Dawn