The spelling usually used for the lasagna dish in British English is lasagne.
The difference reflects Italian grammatical and regional usage. In Italian, lasagne is traditionally the plural of lasagna, referring literally to multiple pasta sheets. Northern Italian usage commonly applies the plural form to the baked layered dish, and that convention influenced British English, where lasagne is the usual spelling.
American English more often uses lasagna, following southern Italian singular usage. English treats the dish as an uncountable noun, however, so both lasagna and lasagne can function grammatically as singular names for the food. The British preference is therefore a usage convention, not a distinction between two separate recipes.
The word has a long history. Medieval Italian references include a 1282 mention in the Bolognese Memoriali and a 1284 reference to lagana cum caseo. The earliest recorded recipe, in the early-14th-century Liber de Coquina, described boiled pasta sheets with cheese and spices rather than the tomato-rich layered casserole familiar today. Tomatoes became part of European cooking only after the 15th-century Columbian exchange.