I know these 'late' people from the time I was the boss of 50 employees... There were a few persons they were always late..
When I spoke to them seriously about this things, mostly the result was (for me) very easy: e.g. buying a louder clock or taking an early train... and it works!
So as you say.. just talk to this 'late' people about the topic! It will help...
Of course, talking about issues are the best way to solve them!