There is nothing inherently unhealthy about a ketogenic diet. In fact they are often prescribed to children with epilepsy. Although total cholestrol does rise is some, overall lipid profiles (ratio of hld to ldl) improve.
Like any diet, food choices are important. For fats go with organic grass feed butter, coconut oil, fish oils, avocado, nuts and seeds. Protein should be predominately from cage free whole eggs, grass feed beef, chicken, and some high quality protein powders. There is little issue with eating green and leafy vegetables so load up on asparagus, red and green peppers, zucchini, broccoli, cauliflower, etc.
As long as total "usable" carbs (less fiber) stay under 30gm per day, you will stay "ketogenic".
Again, this would not be ideal for performance without periodic carb refeeds. From solely a health perspective it could be continued indefinitely.