You can configure the mapping like so:
Mapper.CreateMap<Assay,AssayDto>()
.ForMember(dto =>
dto.Genes,
m => m.MapFrom(a => GenesList // your separate list of genes
.Where(g => g.AssayID == a.AssayID)
.Select(g => g.Name)));
BTW, personally I always prefer this shape of statements:
dtos = assays.Select(a => Mapper.Map<AssayDTO>(a));