Clearly lake salinity increases in both cases, but the rate at which it increases depends on the salinity of the lake.
If the salinity of the lake is less than that of sea water, (see figure 13), closing the mouth keeps the lake fresher at least until the lake salinity reaches that of sea water again.
If the salinity of the lake is greater than sea water, (see figure 14), then closing the mouth results in a faster rise in salinity.