Over millions of years silt washed into a lake formed layers of sedimentary rock. What type of rock was likely formed?

If silt washed into the lake formed it will results into formation a kind of sedimentary rock.

In fact it will be a kind of detrital or castic sedimentary rock.

This is also called as siltstone rock.

The classification is based on grain size as it is silt size it is known as siltstone rock

The answer is; siltstone

As the sediments accumulate in layers over time on the ocean bed, the pressure of the sediments above causes the layers to compact together and become cemented into siltstone rock. Other types of sedimentary rocks that may form in this process (depending on the size of grain) is sandstone and shale.