You have two levels of possible correlation.The only independent measures you really have are from each of the 6 laboratories.
My understanding of the way you presented your problem is that among the 6 labs:
Day 1: 6 measurements
Day 2-6: 2 measurements per day
So in total, you have 18 measurements from each lab, which totals 108 obs. Is that correct? If so, are you aware of GEE models?