You are more than welcome to bring your own food into the Park. As LEGOLAND Windsor Resort is predominately an outdoor attraction, there are limited covered areas outside to each lunch. It would be down to the discretion of duty managers within each restaurant if you were able to take food into the restaurant when it is raining, however this cannot be guaranteed.
If you wish to bring in a picnic/cool box, I would advise for you to leave the cool box in the car and then obtain a hand stamp when you exit to allow you to collect it at lunch and return it to the Park. This is because the lockers are too small for a cool box and Guest Services are unable to store food.