What are these lines on this stone?
You don't say which lake, but these are almost certainly crinoid stem fossils. Crinoids, or sea lilies, are echinoderms (relatives of starfish and sea urchins) that anchor themselves to the sea floor and feed on plankton.

In some crinoids, the animal's sea urchin-like calyx is connected to the anchor by a long stem to a holdfast which anchors it. The stem part of the crinoid's endoskeleton is a stack of calcareous rings or pentagons (called "ossicles") which look almost like a little spinal column. (However, vertebrates are not descended from crinoids, even though Echinoderms are deuterostomes, placing them closer to chordates than arthropods or molluscs). 

When the animal dies, it falls into the bottom sediment and the stem can become disconnected as the sediment is compressed into limestone. Sometimes the rings stay aligned, and show assemblages like you see in your rock. Other times, all you see are disconnected rings or little pentagons, like the ones all over the rest of the rock.

Crinoids have been around since the Ordovician period 
485 million years ago, so they appear in (and sometimes entirely make up) limestones throughout the world.



Source: GeoKansas

And, just because it's there, here's  a video of a crinoid crawling across the sea floor.