Lavilla's Airwaves Ducati team-mate Leon Haslam twice finished second after leading at the start of both races. Lavilla, the reigning champion, now has a 36-point lead but he played down his title chances, saying: "I am not thinking of the title. Last season Ryuichi Kiyonari won the first six races but not the title."
The Spaniard may be cautious off the track but there is no doubting his current form after he set a 113.25mph lap record at Thruxton.
"It's hard making the start, and then seeing him come past," said Haslam, who is second in the standings. "But he has not put a foot wrong, and I am struggling a bit still with my ankle injury," added Haslam, who was injured in a crash in round one at Brands Hatch.
Kiyonari took third place in the opening race at Thruxton. He looked set for an action replay, but his HM Plant Honda team-mate Karl Harris denied him a second podium finish.
Harris escaped injury in a start-line incident in the first race but took third from Kiyonari in race two at the chicane on the final lap.
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