sankoku: 
獅子
1. ライオン
2. 唐獅子。特に唐獅子舞の面

唐獅子
中国で、ライオンをもとに考えた想像上の動物。しし。からしし。

https://en.wikipedia.org/wiki/Komainu
Komainu (狛犬), often called lion-dogs in English, are statue pairs of lion-like creatures either guarding the entrance or the honden, or inner shrine of many Japanese Shinto shrines 

During the early Heian period (ninth century), the tradition changed and the two statues started to be different and be called differently. One had its mouth open and was called shishi (獅子, lit. 'lion') because, as before, it resembled that animal. The other had its mouth closed, looked rather like a dog, was called komainu, or "Goguryeo dog", and sometimes had a single horn on its head.[8] Gradually the animals returned to be identical, but for their mouths, and ended up being called both komainu.[8]

changed "dog" to "lion-dog", added x-ref to 唐獅子.  Added (stone) for consistency, to the extent that [2] is focused on shrine statues.

This edit motivated by my edit of 唐獅子, which seems to generally translate as "Chinese lion". 

sankoku has a circular reference between 獅子 and 唐獅子.

If we gloss the x-ref 狛犬 with the "dog" kanji as "lion-dog", surely 獅子 "lion" counterpart merits being at least a lion-dog as well. (if not a lion outright)

It seems possible to me that [2] is perhaps overly specific (or that we need [3]: Chinese guardian lion). The shinto stone lions are just one place that 獅子 appear in Japanese culture.

Numerous references indicate that:
1. shishi came first to temples
2. then we had shishi on the left, komainu on the right
3. shishi and komainu took on each other's characteristics until they were nearly indistinguishable, except that shishi is always on the left, with its mouth open, and the komainu appears to the right with mouth closed.
4. They are both just called komainu today. (which is why the 狛犬, confusingly, does not say "right-handed" stone lion-dog. It now covers both).

@@ -27 +27,3 @@
-<gloss>left-hand guardian dog at a Shinto shrine</gloss>
+<xref type="see" seq="1663630">唐獅子</xref>
+<xref type="see" seq="1663630">唐獅子</xref>
+<gloss>left-hand (stone) guardian lion-dog at a Shinto shrine</gloss>

Google N-gram Corpus Counts
╭─ーー─┬───────────┬───────╮
│ 獅子 │ 1,048,939 │ 99.2% │
│ 師子 │     8,643 │  0.8% │ 🡠 rK (daijr, koj)
│ しし │ 1,231,788 │  N/A  │
╰─ーー─┴───────────┴───────╯

@@ -10,0 +11 @@
+<ke_inf>&rK;</ke_inf>

@@ -18,0 +19 @@
+<xref type="see" seq="1137760">ライオン</xref>