Unfortunately, "He was late at the meeting" is non-idiomatic usage to a native English speaker. Here are two constructions that would work using your examples (please note that neither is a "that-clause").
"Since he was late arriving at the meeting, we couldn't start our discussion on the security of the IT systems."
"We couldn't start our discussion on the security of the IT systems, because he was late getting to the meeting."
When using a "that-adverbial clause," it is important to make sure it modifies the verb rather than a subject. Here is an example.
"That he was late for the meeting was irritating, but it was not the reason we fired him."