low and high tides in a lake...........?

As written above, lakes don't have a tide. The reason is simply this: in order to have a tide of some significance, the water must be able to move to and fro in a harmonic way between either a diurnal frequency of 24 hours and 50 minutes, or a semi-diurnal frequency of 12 hours and 25 minutes.

The tide is the result of the gravitational pull of the moon, for about 65 percent and the sun, for 35 percent. In places like the Bay of Fundy, it moves up to 17 meters (the world record) and in the English Channel, up to 11 meters near the French harbour of Paimpol. But in the Oslo fjord of Norway, where I live, it is barely 15 centimeters!

Even a large lake would be too small to see the water to move in such a long period of time. To understand the tide, try to do this:

Take a wide container such as a flat pan, half full with water. Rock the container between your hands. See how the water goes from one side to the other. Increase the rocking period and notice that when you come to a harmonic period, the water will spill over the edge.

If you move your location to a coastline, in your story, remember that the high water will happen about 50 minutes later for each day. This is also the time delay the moon rises in the sky each day. This is because the moon orbits the earth in about 28 days.

Good luck with your story.

Lakes on Earth don't have tides. That only occurs in the oceans and to a quite small and barely measurable extent in certain very large seas such as the Mediterranean.

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It should since the tides are influenced by the moons gravity.