late
1.是形容词,晚的,已故的等意思很多.如：He is always late.
2.副词,He comes late.
lately是副词,近来,不久前.
如：He comes here lately.他最近会来到这里
latest
1.是late的最高级,最晚的,最新的.如：This is the latest news
2.是名词,最晚的,最新的.如：I want the latest.
later是
1.late的比较级,较晚的,更迟的.如：I get up at 10,he is later than me,at 11!
2.副词,后来,稍后,一会.如：Try again later 稍后再打
以上不是很详细,不过可以帮助你理解.