来不及 has two meanings,one means" have no time to do something", e.g. 我来不及去参加聚会了。means I wouldn't go to the party, because I have to go for something urgent.
the other means" there is little time left ", to remind people hurry up. e.g 快点!来不及了!
迟到means late, for late a bit:迟到了一会儿; for N minutes late: 迟到了n分钟; for huge delay:迟到了很久。
来晚了 the same meaning and use with 迟到, but it's more colloquial.