Two worn cam lobes

Can be a couple things that cause it. The most common issue is that the oil to them was blocked by sludge or a bit of dirt and the lack of oil allowed metal to metal contact. This would be the item I would suspect if the car has been running okay and then suddenly developed this over a few days.

The next most common reason is that the parts were made with poor heat treatment and every time the engine was started and before the oil started flowing, the parts would rub and grind on each other. After a while the cams poorly heat treated surface failed and the softer metal underneath started wearing.

Thank you for the reply.
Last year my cam belt snapped, two valves bent and one rocker broke. The head was done over, new valves and new rockers, valve stem seals as well. The car was running fine until a few weeks ago, ticking noise and today discovered the cam lobe worn. The lobe was worn in the same place where the previous rocker broke.

Where do I start please?

That would have started the process then, it does not take a lot to damage them. The wear in one lobe is probably more than the other as well. I suspect that the damaged lobe started wearing first and started heating the cam which caused the second lobe to start failing. Once through the hardened layer it does not take long for a camshaft to wear down.

As the head was rebuilt last year I would probably do a very good flush of the oiling system and make sure the passages are flushed and replace the cam and rockers with new. The metal should have been removed by the oil filter so cleaning the passages to remove any that is in the drain system and the oil pan should clean it enough. Then once you have it running again I would probably use some cheap oil and a new filter to run it until it warms up, shut it down and change the oil and filter and then just monitor the oil pressure.

This is very helpful and all makes sense.
I did oil change the day before and changed the filter hoping the tappet noise would be gone, but when I started car it was still there and that is when I removed the tappet cover to see the damage.
Which oil would be the best for my car?
I put Shell Helix X5 15w40 in two days ago.
Can I still drive with it until I replace all the parts?
Will anything else get damaged if I carry on driving the car until month end?

The only issue with driving it will be more metal getting into the system. Ideally you want to limit that because it will wear things like the bearings and other lubricated parts making the list of parts you need to replace longer and reducing the remaining life of the engine. The other option if the body is in good shape and the rest of the vehicle is good would be to source a replacement engine. But at the moment you should be able to save this one.

As to the oil, I would run whatever is called for, I am not a fan of second guessing the folks who designed the engine.