How long/ late can an employee be before they are terminated?

My employee was suppose to come in yesterday at 11:30 and didn''t arrive until 2:50 with the excuse that he had to rearrange his schedule. He didn''t notify me. Today, he left for lunch at 12:30. It''s now 3:25 and he hasn''t returned. My office manager and I both called him once and each sent him a text message. We haven''t received a response. He''s in his first 90-days of employment, signed a handbook that clearly states lunch breaks are 45 minutes and we are to be notified if someone is going to be late to the office.