If they are lying, they'll be punished.
Valid, but it means "If they are lying [as of now], ...". This is different from "If they lie, ...", which can be called the use of the generic present, which is not constrained to the past, present or future, because it can be used when referring to past speech, presently ongoing speech, or future speech. The present continuous "are lying" can only refer to speech up to the present (including ongoing speech).
If I'm meeting them, I'll let you know.
Valid, but it means "If I decide to meet them, ...". I'm not sure why, but it could be because "am meeting" here refers to the point (possibly in the future) at which the decision to meet was made. Strangely, I cannot quite pin down the reason this does not apply to the previous example, but I've native speaker certainty.
If you were meeting them today, you would have gotten to know them better.
Valid, but probably not in the context you want. The "would have gotten to know ..." states the definite outcome under a given possibility in the past, and so the "were meeting" has to denote such a possibility in the past. It cannot simply mean "If you [had] met them today", because then the meeting would be conceptualized as a single event. Instead it would probably mean "If they were the ones you were meeting today, ...".
If I had been talking with him, I would have told him.
Valid, and normal, because "had been talking with him" describes a possible past situation (of having been talking with him), under which it is claimed that "I would have told him". Note that it conveys a different meaning from "If I had talked with him, ..." which simply refers to the past event of talking with him.