This report shows the locations in 1963 of LIMITED and LILYRIC. Note how their positions had switched by 1967: https://maryferrell.org/showDoc.html?docId=39230#relPageId=3&tab=page
A table called "Soviet photo coverage from LIMITED base" for the months of September and October 1963. It shows that the first photo on 9/27/63 at LIMITED was at 10:18 am and the last one was at 11:46 am. It also shows that LIMITED was not operating on Sept. 28.
John Newman, Osald and the CIA (2008 edition), pp. 356-357
Newman's table shows that the only reported visits by a man called Oswald to the Soviet embassy was at about 12:30 pm on 9/27/63 and about 9:00 am on 9/28/63 The last photo taken by LIMITED on 9/27 was allegedly at 11:46 am, and it was not operating on 9/28. Therefore, if the records are accurate, Oswald could not have been photographed by Oswald during his stay in Mexico City.
During 1959-1960: "LIMITED is used as a radio dispatch base in addition to physical surveillance of persons entering the front gate. Their photography is negligible compared to their other duties. The LILYRIC base performs the best photography of persons visiting the front gate, perhaps because the vantage point for taking the pictures is from the second floor and above the street traffic which partially blocks LIMITED photographs."
4/30/64 from COS Win Scott to C/WH J.C. King: "Also worth mentioning at this point is the radio "dispatching" of the LIEMBRACE team by the LIMITED base." To evade the tight security of the Mexican police around the Soviet embassy, the "LIMITED radio operator dispatches the team onto target personnel giving direction, means of travel, and description of dress of these targets. This permits the team to commence its surveillance a number of blocks from the (Soviet) installation and beyond the protective ring of the local police."