Hi. I've had a look and found a few things for you. Mary King buried 20th Feb 1886. From scan of burial register :-
Mary King of 65 Princess Street, St Peter at Gowts (which is towards the bottom end of the High Street), buried 20th Feb 1886 age 76 ceremony performed b William Croft Catholic Priest. In unconsecrated plot.
Patrick King of 1 Salthouse Lane, St Peter at Gowts. Buried 6th April 1901 age 95 Ceremony performed by William Croft Catholic Priest. In unconsecrated plot.
There is a 3rd person in the grave - don't know if there is a family connection at all.
Arthur Emmanuel Loewental of Wellingore Old Vicarage. Buried 19 Nov 1964 (didn't check the scan of the burial register as it's pay to view). His wife Rosa Katherina J Loewental of West Parade Lincoln buried 5th Feb 1958 she in the next door plot D794. I did find her probate record attached. Her husband was an artist - interesting. No trace of probate record for him.
If D 795 is a shared grave ie the Kings didn't purchase the grave plot it's unlikely there's an MI. It's not listed on the Lincs MIs on FindMyPast but the Bereavement services of the council who operate the cemeteries should be able to tell you -
bereavementservices@lincoln.gov.uk they're very helpful and if you arrnage it beforehand they'll usually arrange for someone to take you to the plot and show you where it is. Hope this helps. Enjoy your visit to LIncoln . Kind regards Penny