OK, chewed over this some more and this is my reading/summary so far -- open to further suggestion/correction!
One error which I realise I may have made is re Mary Lole's will and Cornelius Lole/Sarah Gibson. Did she describe them as cousins or as nephew/niece? I can't remember and I can't find my jottings. Either way though, I think it was generationally flexible as Sarah seems to have been Cornelius' niece, so they were of different generations.
That aside it looks as though we have the following:
1674 - Christopher Lole's will proved Laughton
also 1674 - John Lole, son of Christopher of Laughton, is apprenticed to a haberdasher in London.
(I wonder if C's will left money to cover J's apprenticeship?)
so John was probably b around 1660ish?
John Lole, haberdasher of London, named as paying tax for an apprentice in 1813.
John Lole, haberdasher, of London - will proved 1733 - names (amongst others) Daniel and Cornelius Lole (?relation to him?), and his brother William of Laughton, who has an unnamed wife. William gets £10 and clothes; Daniel gets a coat; D and C both get some money for a ring.
Cornelius Lole, gentleman of London, marries 1760 aged 40. Will 1780 gives his property at Laughton to his brother Joses Lole; also names Benjamin Sims of Marston, Northants, and cousins Timothy and Joseph Sims.
Meanwhile William Lole yob around 1697 m Mary Roper in Kibworth in 1730. William leaves everything to Mary when he dies in 1765; Mary mentions various cousins, or nephews and nieces, including Cornelius Lole and Sarah Gibson, in her will in 1770. Wording suggests C is from Walgrave, Northants, but I will check that. Sarah was def living there by then, Sarah Lole having married John Gibson.
Cornelius's brother Joses is in Laughton by 1754 but records don't go back further than this for Laughton. He and his wife Mary have several children named above, earliest baptism being 1754 (but probably had at least 1 child - Sarah - before this). Joses's will names his children and sons in law.
There are other Loles in London in the late 1600s but I can't see a Leic connection.
I hope to go to the records office again within a fortnight so will double check Mary's will and also have another good look for Christopher's will from 1674; and anything else I can find!