"If you're on time, you're late" is an expression that resonates with those of us who so value punctuality that we almost always arrive early.
Arriving late may work for some social receptions and parties but never for a business appointment.
At the same time, cooling your heels in a lobby 15 or 20 minutes before a meeting is strange and excessive. [If you're that early, stay in your car and read or review your plans for the meeting.]
Culture, of course, makes a difference. I recall being told in the Army that if you are scheduled for a 3:00 social event at a general's home, you ring the doorbell at 3:00.
Not at 2:59.
And certainly not at 3:01.