“Lasagna” can mean both:

• The pasta: plural lasagne (Italian) or singular lasagna (English) — the wide, flat sheets used in layered dishes.
• The dish: layers of pasta, sauce, cheese (and often meat or vegetables) baked together — commonly called lasagna in English.

So context and regional usage determine which sense is intended. (See Oxford English Dictionary; Italian usage distinguishes lasagna [singular pasta sheet] vs. lasagne [plural/pasta sheets].)

If I must choose one: “lasagna” most commonly refers to the baked layered dish. The pasta sheets are technically “lasagne” (Italian plural) or simply “lasagna” in English usage, but everyday use usually means the meal. (See Oxford English Dictionary; Italian usage distinguishes singular/plural.)