L&M say “milk, whey, cheesecakes, etc” were sold here. In the 18th century it was known as Cheesecake House. It was located on the north bank of the Serpentine, but it no longer exists. There is more information at Pastscape and also on this 18th century map.
The overlays that highlight 17th century London features are approximate and derived from Wenceslaus Hollar’s maps:
Open location in Google Maps: 51.505939, -0.166021
The "Lodge" is but another name for the "Cheesecake House" or "Cake House," or as it was sometimes called from the proprietor, the Gunter of those days, "Price's Lodge." This house, which was a picturesque feature, stood near the Ring, on the site of the present building of the Humane Society, and must have been the scene of many amusing incidents in the lives of those who graced the Ring, in the seventeenth and eighteenth centuries. A little stream ran in front of it, and the door was approached over planks. White with beams of timber, latticed windows, and gabled roof, a few flowers clustering near, with the water flowing by its walls, the old house gave a special charm and rural flavour to the tarts and cheesecakes and syllabub with which the company regaled themselves. [Land in Hyde Park given by George III to the Humane Society in 1794. An old farmhouse on the site is used to give medical treatment to the rescued. It was damaged by bombing in 1940.
Read more: http://www.gardenvisit.com/book/london_parks_and_…
Photographic Print of View of Cheesecake House in Hyde Park, London, 1795. from Heritage-Images http://www.amazon.co.uk/Photographic-Print-Cheese…
The Lodge shows on the S of Hide Park Corner near the left side of this map
Try https://georgianera.wordpress.com/2018/09/18/the-… for the Cheesecake House as the earlier links now (April 2021) have gone dead.
Chart showing the number of references in each month of the diary’s entries.