One of the major differences between chronically punctual and late people is how each group perceives earliness. Those who are on time will aim to get to a place earlier just in case anything goes wrong in the journey, while those who are late see being early as a waste of time and aim to get there almost just on time.
To switch this mentality, think of ways to make being early more valuable. You can use the extra 10 to 15 minutes to read, check emails or grab that much needed cup of coffee next door. Being early is being constructive.