There is a druid in the 5e Monster Manual Appendix B: Nonplayer Characters. None of the other NPC names are class names. For example there is an "archmage" and "mage" (both with wizard spells), but not a "wizard"; an "acolyte" and a "priest" (both with cleric spells), but not a "cleric". This suggests that the NPC names in Appendix B are terms used in the game world. We can therefore conclude that "druid" is both a rules term for a class and a term used in the game world. The lizardfolk shaman casts druid spells. There would therefore be no difficulty in calling the lizardfolk caster a druid.
Why then is the lizardfolk caster a shaman? Because "shaman" is only used in D&D to refer to NPCs and monsters, not PCs. It does not appear in the PHB. But why should the word be used in this way?
The PC druid in the PHB is described as a "priest of the Old Faith, wielding the powers of nature". The "Old Faith" usually refers to pre-Christian European religion. The historical druid was a pre-Christian Celtic magico-religious specialist. In popular culture "shaman" is associated with non-European (particularly Native American) magico-religious specialists who communicate with nature spirits. This is how it is used in
Robert E Howard’s Conan stories, which are cited in Appendix N of the 1e DMG and Appendix E of the 5e PHB.
Lizardfolk live in "swamps and jungles". Europe is not known for its jungles. Lizardfolk lure trespassers "into the lairs of crocodiles". Crocodiles live only in hot climates - the tropics and subtropics. They eat and sacrifice sentient beings, tropes which have, over the last 300 years been attached largely to non-Europeans, especially sub-Saharan Africans, Native Americans, and Pacific Islanders. According to TVTropes the
Cannibal Tribe trope refers to "dark-skinned, non-Christian native tribes".
Lizardfolk have shamans instead of druids because they’re not European.