THERE IS A LACK OF IN-PERSON COMMUNICATIONS IN A SOCIETY.
or
THERE ARE A LACK OF IN-PERSON COMMUNICATIONS IN A SOCIETY.
That sentence is strange and ungrammatical. The answer to your question is that only "there is a lack" is correct. Try simplifying the sentence, and consider using "interpersonal communication" instead.
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That sentence is strange and ungrammatical. The answer to your question is that only "there is a lack" is correct. Try simplifying the sentence, and consider using "interpersonal communication" instead. Also, are you referring to a particular society or to society in general? Post below.