Popierson
Obviously you are familiar with
https://civilrecords.irishgenealogy.ie/churchrecords/civil-search.jspso this is the burial you mention
https://online.belfastcity.gov.uk/find-burial-records/BurialRecordDetails.aspx?RecordID=6279.35839and this the headstone image
https://belfastcity.plotbox.io/static/images/plots/belfastcity/115086/18849.jpgfrom
https://discovereverafter.com/search-results?search_first=julia&search_last=lee&p_sname=on&county=2Census shows not only that Julia was a Schoolteacher but Evelyn a Monitoress 'a female student who helps keep order or assists a teacher in school'.
1911 census. Additional Pages: 2. image confirms house number as 140 Cliftonpark Avenue, a large Victorian terrace, is still there (just, was boarded up 2008 & 2 adjacent have been replaced if look back in time)
https://goo.gl/maps/fohqSjh2oUos6GNT7.
The transcription errors on the names for both Julia & Nora mentioned previously by huey1 & Sinann [replies 1 & 2] have not been corrected for the 1901, obviously no one doing them since John Grenham stopped March 2019.
https://www.johngrenham.com/blog/2019/03/25/my-census-correcting-comes-to-an-end/Strange gap in births, though see there were no other children from GRONI index which includes mother's maiden surnames. James was in Belfast in the same area the entire time - confirmed from street directories on PRONI so whilst the Belfast Council burial & death cert for Robert shows Grays Hill, Bangor that must have been a very temporary posting (or summer holiday) as Street Directories record him at 71 Benwell Terrace, Oldpark Road 1892, 1894, 1895, 1896, 1897, 1899, 1900, 1901 + the daughter's births. Recorded as Principal of Argyle Place School from 1897.
James Mitchell Lee (Martin) 17 May 1884 at 60 Perth Street (off Old Lodge Road, behind Crumlin Road Courthouse).
Julia Evelyn Anna, Robert Bertram & Norah at 71 Benwell Terrace a block of terrace houses on the OLDPARK ROAD opposite Benwell Street (or Hillview Street as it is now).
# James Mitchell Lee & Julia Anna Martin married Eglinton Street Presbyterian 25 July 1883; fathers James Lee & James Martin, both full age = over 21.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1883/10938/5997453.pdf"Return showing the Ages and Length of Service of National School Teachers in the service of the Commissioners of National Education on 31st March 1905, and where furnished, their places of education"
https://www.nationalarchives.ie/article/list-of-teachers-employed-by-the-commissioners-of-national-education-on-31-march-1905/pdf page 7: Lee, James Mitchell, aged 45 yrs, 6 mths (on 31 Mar 1905). Length of Service 26 yrs, 7 mths. Educated MAGHERAFELT No2 Boys, Magherafelt. [Teacher] Training College = Marlborough Street [Dublin]. Serving Co. Antrim in Argyle Place as Principal = Argyle Place National School. [Magherafelt gives you bit more precise location than the 1901 census born Co. Derry].
Julia was Assistant Teacher same school, aged 49 yrs, 10 mths and educated Model School, Belfast; she did not attend a Teacher Training College but had served as a teacher for 34 yrs 4 months (longer than James so presumably a pupil teacher eg at 14-16).
URNEY Street (off Shankill Road) left hand side: Argyle Place Mixed N.S. - Principal, J. M. Lee then 2,4,6 etc / Surnames A-Z: Argyle Place Mixed N.S. - J. M. Lee, principal, Urney Street
https://www.lennonwylie.co.uk/tuvcomplete1907.htm Recorded as Principal there 1907, 1908, 1909, 1910 & 1912 Directories, after than someone else, so slight delay in the name change after his death.
So school was beside/behind Argyle Place Presbyterian Church on Shankill Road, with Argyle St on the other side of the church. Now = "West Kirk Presbyterian" & the two streets have disappeared either side of it
https://goo.gl/maps/9nWPf7NW5Xi6rDR6A ]
The Education (Ireland) Act 1892 made attendance compulsory from ages 6 to 14 in urban districts, extended to rural districts by the Local Government (Ireland) Act 1898. However, there were many exemptions and enforcement was patchy. Previously pupils typically left 12-13.
Between 1843 and 1867, a network of 26 interdenominational District Model Schools was established
‘to promote the united education of Protestants and Roman Catholics in Common Schools; to exhibit the best examples of National Schools; and to give preparatory training to young teachers."
some lengthy background:
https://www.qub.ac.uk/sites/irishhistorylive/IrishHistoryResources/Shortarticlesandencyclopaediaentries/Encyclopaedia/LengthyEntries/Education/https://mural.maynoothuniversity.ie/9689/1/TW-National-2016.pdfNational School Register records are held by PRONI - likely find your grandmothers in it, but is just name, age, residence, years attended & days attended + score in reading writing etc so won't reveal anything new.