Encounter at Farpoint
PICARD: We question whether this court is abiding by its own trial instructions. Have I have permission to have Commander Data repeat the record?
Season 2 Unnatural Selection
PULASKI: Commander Data is an android, Doctor. He is unaffected. As for me, I chose this. I was convinced the children were safe.
Season 2 Measure of Man
MADDOX: I was afraid this might be your attitude, Captain. Here are Starfleet's transfer orders separating Commander Data from the Enterprise
Season 3 Most Toys is interesting
PICARD: Captain's log, supplemental. As the result of a yet unexplained shuttle explosion, Lieutenant Commander Data has been lost.
OBRIEN: I'm reading a weapon in transit with Commander Data. It seems to have discharged, sir.
Seems when it's more formal the full "Lieutenant Commander" is used, but it has to be very formal, usually in Captain Logs (but those aren't exclusively Lt Cdr, nor is Lt Cdr only used in very formal cases)
Even the Computer is in on the confusion
Season 1 Encounter at Farpoint
ENSIGN: This way, sir. You must be new to these Galaxy class starships, sir. (to wall) Tell me the location of Commander Data.
COMPUTER: Lieutenant Commander Data now located in Holodeck area 4J.
Season 4 Brothers
PICARD: Computer, locate Lieutenant Commander Data.
COMPUTER: Commander Data is on the main Bridge.
I think the computer is there to wind the crew up.
Season 6 - Relics, Data introduces himself correctly (of course)
DATA: No, sir. I am an android. Lieutenant Commander Data.
But Even in Insurrection when Data is not obeying orders,
CURTIS: Commander Data, stand down. That's an order. I repeat, stand down!
Data however was almost always proper when referring to himself
11001001:
DATA: Based on all information presently available, the decision is correct. This is Lieutenant Commander Data speaking for the Captain. Abandon ship. This is not a drill. All personnel. This is not a drill. (around the ship) I say again, abandon ship. All personnel, this is not a drill.
Home Soil:
DATA: Bridge, this is Lieutenant Commander Data. No need to beam me up, sir. The situation is under control.
Symbiosis:
DATA: Engineering, this is Lieutenant Commander Data. Bring all systems online and direct full power to the shields.
Conspiracy:
DATA: Computer, this is Lieutenant Commander Data. Please access all Starfleet Command orders to starships, starbases and colonies for the past six months.
Schizoid Man:
DATA: Lieutenant Commander Data
However in Unnatural selection he referred to himself as "Commander Data"
DATA: Enterprise. Commander Data ready to beam aboard.
By Ensigns of Command he was back to normal
DATA: That is correct. I am an android. I am Lieutenant Commander Data of the Federation Starship Enterprise.
DATA: Lieutenant Commander Data of the Starship Enterprise.
DATA: Lieutenant Commander Data to Enterprise. I am preparing to leave Tau Cygna Five and await rendezvous instructions.
Last use of Lieutenant Commander Data was (of course) by Data in Gambit Pt 2
DATA: Open a channel. This is Lieutenant Commander Data of the Federation Starship Enterprise.
Last use by a human was Starship Mine, but he was being introduced to a higher ranking officer so makes sense
RIKER: Mister Data, I don't know if you've had a chance to meet our host, Commander Hutchinson. Call him Hutch. Lieutenant Commander Data, our second officer.
Aside from then it was Silicon Avatar
RIKER: Lieutenant Commander Data was there, yes.
On the whole, Data was referred to as Commander Data rather than Lieutenant Commander Data 78% of the time. The Computer specified Lieutenant Commander Data 6 times and Commander Data 4 times.
The bigger question is why Data never got promoted, in 14 years. He was due to take over from Riker as first officer of the Enterprise in Nemesis, surely that means he'd have had a promotion then?