Select() method works as projection. So it always will return class with properties.
so your lambda expression should look like by that way
if (!string.IsNullOrWhiteSpace(utility))
{
submissions = submissions
.Where(s => s.SummaryBillMaster.BillingGroupFacilityCollection
.Where(p => p.Pipeline.PipelineName == utility && p.Period == s.Period))
.Select(f => f.Facility.DealCollection)
.Any()
);
}