What are mouse LS cells?
Not an easy question, but I got some references about it.
Mouse LS cells are Fibroblasts growing in suspension culture, the paper in reference 1 has this paragraph in its Materials and Methods section:



This cell line seems to be in culture since the 1940s, as the reference to Sanford, Earle and Likely, 1948 suggests. Digging up this reference (number 2 below) tells a bit more about the isolation:


  The cells of this study were from Earle's strain
  L (6), which originated from normal, subcutaneous,
  connective tissue of an adult C311 strain
  mouse.


Reference 6 in the Sanford et al. paper is:


  EARLE, W. R.: Production of malignancy in vitro.
  IV. The mouse fibroblast cultures and changes
  seen in the living cells. J. Nat. Cancer Inst, 4:
  165-212 (1943).


which gives no further details. It is a methodic paper which analyzes the conditions necessary for cell culture - interesting on a historical point of view, since the techniques where developed at that time. The full PDF is linked in reference 3.

About the name I need to speculate a bit, but since the original cells where named "Strain L", and LS cells where derived from there to grow in suspension, it might translate into Strain L Suspension cells.

References:


The Uptake of Amino Acids by Mouse Cells (Strain LS) During Growth
In Batch Culture and Chemostat Culture: The Influence Of Cell Growth
Rate
The Growth in Vitro of Single Isolated Tissue Cells
Production of Malignancy in Vitro.