However, the easiest thing to do would be to get the birth certificate of John Robert Robinson, Dec.1867 Lincoln 7a 444.
Modified - Getting the birth certificate would not only give his father's name,
... assuming of course that there really was a William Robinson

Actually, there was a William ROBINSON aged 30 buried in Lincoln in 1868 - he had died in Hanley, Staffordshire.
Deaths Jun 1868
ROBINSON William 30 Stoke T. 6b 91
and whaddayaknow - there was a William ROBINSON 23 Printer and Compoitor born Lincoln in Hanley in 1861 with wife Elizabeth 25 and son Edward J aged 1. (all born Lincoln)

Perhaps this couple
Marriages Jun 1859
HOLDEN Elizabeth Lincoln 7a 897
ROBINSON William Lincoln 7a 897
There was a John R ROBINSON aged 3, grandson in a BROWN household in Lincoln in 1871.