It depends on the type of lake and its assumed age of formation because based on these facts you can decide which sort of in-situ / authigenic minerals you might expect and use as age-dating target.
For perennial lakes which normally have a reducing environment you can use the radiocarbon dating method for C-bearing organic matter and carbonate minerals, if the sedimentary units cover the Holocene and Late Pleistocene, with OSL (optically stimulated luminescence) you can extent the dating to the Plio-Pleistocene border using quartz and feldspar. Here you have a chance to get an overlap with U-bearing minerals using the U/Pb dating of uranyl-bearing phosphates and hydro-silicates or the U equilibrium method (800 ka). K/Ar and Ar/Ar can be used for mica but too often they are detrital in origin and less meaningful.
Ephemeral lakes may in addition to the afore-mentioned minerals may also host sylvite and “bittern” (langbeinite, kainite) and, in places, K-bearing zeolites (clinoptilite-K, heulandite-K, phillipsite-K, chabazite-K)
If you know that the sedimentary age of the lake is on the Centennial scale, Pb-210 is recommended. If the sedimentary age of the lake is less than 100 years, Ce-137 is recommended. If the sedimentary age of the lake is tens of thousands of years, C-14 is recommended.
It all depends on the compositional variation of the sediments and their most expected age as per the literature of its surrounding areas because lakes have transported sediments. I really appreciate Prof Harald G. Dill for giving a very extensive and precise answer.