Specific mechanism behind lethality of yellow coat color in mice
Really interesting question: The lethal yellow mutation (also abbreviated Ay) affects the agouti signalling protein which plays a major role in pigmentation. Heterozygous expression of it leads to the dominant expression of pheomelanin (which is yellow), causing the mice to express this color (among other effects). To understand why it is homozygous embryonic lethal, we need to take a further look at the gene and its organisation.
Agouti is located on chromosome 2 of the mouse genome and downstream of a gene called &quot;Raly&quot; (synonymous also MERC)(Image from NCBI Genes)

The Ay mutation now deletes a large chunk of DNA, removing about 170kb between these genes. This removes parts of the coding sequence of the Raly gene and the complete promoter and (non-coding) exon1 of the Agouti gene and results in a fusion protein in which the agouti gene is put under the control of the Raly promoter. This leads to the expression of Agouti every time when Raly should be turned on.
Schematically, this looks like this (figure 4 from reference 2):

Raly is an RNA binding protein, which is highly expressed in embryonic tissues. The mutation leads to the expressing of Agouti there instead. According to reference 3 this leads to embryos which do not develop further than the blastocyst stage leading to premature death of the embryo.
So in short, the deletion removes the expression of Raly, a protein important for embryonic development. Im homozygous mice this is embryonical lethal, in heterozygous mice this can obviously be compensated. However, these mice tend to be obese and are more susceptible for certain tumors (reference 4).
References:

The embryonic lethality of homozygous lethal yellow mice (Ay/Ay) is
associated with the disruption of a novel RNA-binding protein
A molecular model for the genetic and phenotypic characteristics of
the mouse lethal yellow (Ay) mutation.
Pleiotropic effects of the mouse lethal yellow (Ay) mutation
explained by deletion of a maternally expressed gene and the
simultaneous production of agouti fusion RNAs
The molecular basis for dominant yellow agouti coat color mutations