I know that lakes can be saline without being alkaline, as well as that lakes can be both saline and alkaline (soda lakes). But can there be/are there any non-saline alkaline lakes?
Wadi El Natrun is a depression in northern Egypt that is located 23 m (75 ft) below sea level and 38 m (125 ft) below the Nile River level. The valley contains several alkaline lakes, natron-rich salt deposits, salt marshes and freshwater marshes.
Lonar Lake, also known as Lonar crater, is a notified National Geo-heritage Monument, saline, soda lake, located at Lonar in Buldhana district, Maharashtra, India. Lonar Lake was created by a asteroid collision with earth impact during the Pleistocene Epoch. It is one of the four known, hyper-velocity, impact craters in basaltic rock anywhere on Earth. The other three basaltic impact structures are in southern Brazil. Lonar Lake has a mean diameter of 1.2 kilometres (3,900 ft) and is about 137 metres (449 ft) below the crater rim. The meteor crater rim is about 1.8 kilometres (5,900 ft) in diameter.
The list of alkaline lake showing salinity and PH is available online, https://en.wikipedia.org/wiki/Soda_lake#List_of_soda_lakes
Majority of the alkaline lakes are having salinity, but their rages vary. The
soap lake is a meromictic soda lake in the town of Soap Lake, Washington formed by the Missoula Floods at the foot of the Grand Coulee. It is having relatively low salinity.