Please don't post projects to some cloud services, upload them directly here to the forum (--> Attachments and other options). This way the attachment will still be available even after you deleted the project from that other cloud.
And it would be helpful if you'd remove unneeded dependencies (ATFlatControls) from the test project. Remove also the password-protected zip from the uploaded file itself, it is not needed and just confusing.
The program hangs becauses you call Invalidate from your DrawCell Handler. This trigger another drawing cycle which calls DrawCell again which triggers yet another drawing cycle ...
Removing this makes the program responsive again. I assume that when there is a '-' in column "Flg" all cells should be drawn in strike-out style, correct? This does not happen, I'll have to investigate. NiceGrid is not "my" component, but I ported it to Lazarus, and therefore I feel responsible. Basically your idea should be working, but I don't know yet whether this is handled correctly by TNiceGrid.