I would suggest another look at your chart - Lyneham does not have a MATZ, it's a Class 'D' CTR/CTA.
Lyneham normally very accomodating with zone transits - though I'd make sure you stay north of the motorway both ways through as if you get it wrong south of the M4 you could impinge on the circuit.
As for how busy - you can never tell. Depends how many aircraft are away working and how many are available for training.