compatible Shimano 3 speed left shifter (model: ST-EF51-AL)?
That's just a mountain Shimano triple flat bar shifter with a V-brake lever.

You can buy any left hand shifter which is marked for triples from the Shimano mountain lines: Tourney, Alivio, Acera, Altus, Deore. You may need a separate brake lever, which has to be sold for V-brakes and flat bars (it will look like the existing brake lever). Microshift also makes compatible ones, as does SRAM under their Attack! line. You can also use a friction shifter (cheapest option, eg. Sunrace SLM10). 

As an example, you can use the Shimano Acera SL-M310 shifter combined with the Shimano Acera BL-M421 brake lever. 



Go to your local bike shop, and they should have a ton of these parts on hand.