In a saucepan bring the water to a boil, add a tablespoon of salt and cook the tagliatelle. 
Chop finely the onion, thyme and cherry tomatoes and sauté in olive oil in a pan. 

Add all the ingredients for the pesto in a blender except the parmesan. Beat well. Just before you finish, add the parmesan and beat well again to bind the pesto sauce.
Cut the squid into a tagliatelle shape and add it in the pan along with the onion and the cherry tomatoes. 

Strain the tagliatelle from the water and add in the pan with the rest of the ingredients. 
To finish cooking, add the pesto and the lemon zest in the pan with the tagliatelle.