To make the purée, prick the lemons fairly deeply all over and place into a saucepan with cold water to cover. Bring to the boil then remove from the heat and repeat this twice more, using fresh water each time.
In a separate pan bring 400ml water and the sugar to the boil and simmer for 15 minutes to make a syrup.
Place the lemons into a clean saucepan and cover with syrup, bring to the boil, simmer and cook until the lemons are very soft. Remove from the heat and allow to cool in the syrup. Put the lemons with 275ml of the syrup and blitz in a liquidiser for 10 minutes. Pass through a fine sieve, and refrigerate until ready to use.
To make the crackers, purée the squid in a food processor, pass through a fine sieve, then return to the food processor with all the salt, tapioca and squid ink. Blitz well.
Divide the mixture into 10 large vacuum pack bags, roll the mixture out thinly in the bags and seal. Fill a deep-sided roasting tray with hot water and on top of the stove bring the water up to 100°C. Place the vacuum pack bags into the
water for 45 minutes. Remove from the water, allow to cool, and then refrigerate to chill. Once chilled remove from the bag and cut the crackers into roughly rectangular pieces approximately 10 x 5cm in size.
Preheat the oven to 60°C/140°F/gas mark ¼, or as low as possible. Place the crackers onto a cooling rack and into the oven to dry out for up to 24 hours. At this stage the crackers can be kept in an airtight container for several weeks.
To serve, heat the oil in a deep-fat fryer to 190°C, drop in the crackers and they'll puff up extraordinarily. Lift them out of the oil with a slotted spoon and drain on kitchen paper.
Serve the squid ink crackers cold with thin slices of smoked salmon, lemon purée and garnish with a couple of sprigs of sea vegetables.