Hyundai Lantra Engine Problems

I'd be checking the crank angle sensor, a faulty sensor can cause the sort of trouble you're having.

The battery won’t affect it, neither will the starter motor, but new leads and fresh fuel are always worth doing. You could also replace the spark plugs and the coil, and perhaps check the crank angle sensor.

I'd say the battery could be tired and lacking the grunt to crank the engine and power it when the engine is hot. Once it's cooled for a period it doesn't require the same power to crank the engine, so there's grunt left to run the engine as well crank it.

It's not a particular problem of the Lantra, and I would expect it could be fixed. I had a recent case where the engine in a car of another make was shaking at idle; that turned out to be the PCV valve. The valve was replaced and the car ran fine. So check the engine for things that could cause an air leak at idle.