Fill a pan one-third-full with vegetable oil and heat to 180C/350F. The oil is ready when you drop a breadcrumb in and it sizzles. (CAUTION: hot oil is dangerous. Do not leave unattended.)
Deep fry the tortilla triangles in the hot oil for 1-2 minutes, until crisp and golden. Remove using a slotted spoon and drain on kitchen paper.
For the dip, mix the yoghurt, parsley and lemon juice in a bowl to combine.
To serve, arrange the tortillas on a serving plate and serve the lemon dip on the side.