Lawrence penalised the British & Irish Lions scrum three times in the first half and on each occasion the world champions kicked their goals. Those nine points were crucial in the end.
But Meyer believes it could be a different story in Pretoria this weekend when Frenchman Christophe Berdos takes charge of events.
"The Boks used their opportunities to the full, while the Lions missed their chances. But another major factor was the interpretation of the laws and the adaptation to the new rules," Meyer wrote in his column in the South African Sunday Times.
"We had three penalties - nine points -from scrums and, quite honestly, you shouldn't be gifted points so easily in Tests from the set piece. If you look at the maul, they pulled it down, we kicked to the corner and that ultimately led to Brussow's try in the second half.
"Add it up and the Springboks got an effective 16 points from penalties due to the law changes. Having Bryce Lawrence as referee played to our favour because of the southern hemisphere interpretation of the rules - it's going to be interesting in the second Test a French ref takes the whistle."
Meyer also believes that the decision to take open side specialist Heinrich Brussow out of the battle so early in the second half almost turned into a fatal mistake by the Springboks. With the Free State Cheetahs 'fetcher' out of the equation the Lions were able to get some good loose ball to play with.
"A third factor in the match was the way the Lions started playing well in the second half. That was after Brussow was taken off," he added.
"I just believe you need a quality openside flanker on the field all the time. We no longer had a specialist openside flank on the field when he went off and, for the first time in the game, the Lions got quick ball and showed how dangerous they can be.".