On L67 SII 3800 engines concerning LIM gaskets the two prevalent symptoms I've seen and had is coolant in the motor oil not oil in the coolant, although it is possble. Also, no oil in coolant or coolant in oil just a noticable coolant loss and driveability issues. Another possibility would be head gaskets - a leak between a coolant passage and an oil passage within the defective head gasket. Plus unless confirmed through an analysis it could be combustion by-products.
If there is a sufficient quantity of oil going into the cooling system then you may see that by seeing lower oil levels than normal. So accurately check the oil level and condition of the oil for a milky substance and coagulation.
Another scenario I've seen is ATF in the cooling system caused by a bad radiator and not motor oil at all.
These LIM gaskets were replaced due to coolant loss found to be coolant in the oil.
If you decide to replace the LIM gaskets be sure to use the new GM aluminum framed ones. See link below.
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