Lima and Storm broke the old course record of 66 set by Peter Gustafsson and Stephen Dodd last year at the San Roque Club's Old Course.
Both players carded one bogey on the day. Lima dropped a shot on his first hole, but recovered with six birdies and an eagle.
'Seven under is great,' said Lima, whose only other first-round lead came at last year's BMW Championship. 'I am really pleased overall.'
Just minutes after Lima finished off his 65, Storm had a chance to surpass him for sole possession of the lead, but had a 6-foot birdie try at the 18th hole lip out.
'I don't want to get too far ahead of myself, but everything seems to be going in the right direction,' said Storm, who has never held even a share of the first-round lead. 'I have put in the work, and hopefully the rewards will keep coming.'
Raul Ballesteros -- the nephew of five-time major champion Seve Ballesteros -- is among a group of five players who trail Lima and Storm by a shot at 6-under-par 66.
Ballesteros looked like he would crush the old course record when he was 9 under through 16 holes, but he dropped three shots on his final two holes (Nos. 8 and 9) to end one back.
'I got a bit nervous. I was thinking, 'I am 9 under. I've never been 9 under for 16 holes before,'' said Ballesteros, who is playing on a sponsor's invitation. 'It's not my best score. I have had a couple of 61s at my home course in small events, but it is my best result on The European Tour.'
Joining the 25-year-old Spaniard in a tie for third place were Miguel Angel Jimenez, Titch Moore, Juan Parron and Miles Tunnicliff. One stroke further back, 10 players are knotted in eighth place at minus-5.
In all, 46 players are within five shots of the leaders, who began their rounds within 10 minutes of each other.
Lima started on the back nine and was 6 under through seven holes after his eagle at the par-5 16th. He then played his next eight holes at plus-1, carding seven pars and a bogey at the par-4 first -- his 10th hole.
'On the back nine I was a little tired with jet lag after the two events in Asia,' admitted Lima, who went on to reach 7 under with birdies at the seventh and eighth holes.
Storm's round began with consecutive birdies at the first two holes, as well as Nos. 4 and 5. He dropped a shot with his only bogey at the par-4 ninth, but played the back nine at 4 under with birdies at 10, 12, 15 and 16.
Among the players tied for eighth place at 5-under-par 67 is defending champion Peter Hanson, who poured in four birdies and an eagle to go along with one bogey.