"One that has survived is Lattice C, one of the most performant of the compilers tested by Byte. Lattice C was so good that it was licensed by Microsoft and sold as Microsoft C V1.0 before being replaced by Microsoft’s own in-house Microsoft C V2.0 compiler."
"The Microsoft C compiler has interesting historical roots. Although Microsoft itself works with C, this compiler is not a direct Microsoft product. Instead, it is an adaptation of the famous and highly regarded Lattice C compiler."
There are also ads like https://archive.org/details/PC-Mag-1984-09-04/page/n51/mode/... saying "Microsoft C compiler / Includes Lattice C and the MS Librarian".
I can't find info about v2 or v3.
Edit: https://winworldpc.com/product/microsoft-c-c/2x says "Microsoft C 1.0 and 2.0 are a rebranded version of Lifeboat Associates Lattice C", so your doubt seems well founded.