Recently I came across this sentence:
We are having it looked into.
Is it equivalent to "We are looking it" or "We have looked into it"? Kindly help me understand the grammar structure of it.
We are having it looked into.
The meaning is:
Someone is looking into it on our request.
That is, not we ourselves are looking into it, but we requested someone - say, an employee, or an outside specialist, to look into it, and this someone is looking into it now.
It may be that nobody has actually started "looking into it" yet, but we are actively pursuing the goal of "someone's looking into it".
The sentence certainly does not mean "we have looked into it": the process of "looking into it" has not been completed.
"To have someone do something" is a construction that means roughly to cause someone to do something, to make someone do something, or "to give someone the responsibility of doing something":
This construction means "to give someone the responsibility to do something."
Examples:
Dr. Smith had his nurse take the patient's temperature.
Please have your secretary fax me the information.
I had the mechanic check the brakes.
So, Dr. Smith might say:
I'm having the patient's temperature taken.
Your sentence uses a "causiative construction", only it is put in the passive voice, and because of that we are not told who exactly is "looking into" it. The author of the sentence might add a "by-phrase" to make it clearer:
We are having it looked into by our maintenance team.
Related: my earlier answer on causative constructions, with a list of other answers and discussions.