I thought Lamar was Jerome Morrow's father. The only reason I question that Lamar is not Jerome's father is that Lamar speaks with an American accent and Jerome with a British accent. And there's nothing in the movie which suggests why this would be.
However, what makes me believe that Lamar is Jerome's father is the following:
In one of the earlier encounters between Vincent and Lamar, Lamar says something about how he should tell Vincent about his son. This is an unusual thing for a doctor to say to a patient he doesn't know very well, and I guess in the context of the world in which Gattaca is set, this would be strange and yet Lamar feels that he needs to tell Vincent about his son. There has to be a reason for this and my suggestion is that Lamar knew something at this stage about Vincent - in fact, I think he already knew, and how and why I will explain later.
Lamar says that his son admires Vincent. Why would this be in the plot if this son remains completely anonymous? I believe this son of Lamar who admires Vincent is Jerome because after Jerome and Vincent go out and get drunk, when they return and Vincent is trying to put Jerome on the bed, Jerome says to Vincent "I'm really proud of you, Vincent" and I think this is the key to realising that this son of Lamar who admires Vincent is Jerome. Also, what I thought was significant was that Vincent says to Jerome, "You must be drunk to call me Vincent." The real significance here is not that Jerome calls Vincent by his real name but that Jerome, while drunk, spoke what was in his heart, that is, his admiration for Vincent.
Lamar tells Vincent that "for future reference, right-handed men don't hold it with their left. It's just one of those things". How did Lamar know that the real Jerome Morrow was right-handed if he had always thought Vincent was Jerome and Lamar had always noticed that Vincent was left-handed as the above quote reveals. This suggests that Lamar always knew that the real Jerome was right-handed and he could only have known this if he had known Jerome - and further if the real Jerome was in fact his son. The fact that Lamar makes the comment about Vincent's left-handedness takes us back to when Vincent is trying to copy Jerome's signature and he says something like "trust you to be right-handed". It's true that the majority of people are right-handed but the only person we really know for sure is right-handed is Jerome and I think this was put in the movie to flag this connection later on.
Jerome was supposed to have all the genes that enabled him to get into Gattaca. However, he never made it in. But Vincent did. Why was it that Jerome couldn't make it? Because when Jerome and Vincent are out drinking, when Vincent tells Jerome that Jerome should be the one going up into space and not Vincent, Jerome confesses to Vincent that he is afraid of heights. This is his weakness which prevents him from getting into Gattaca. What is suggested here is that acrophobia is not a genetic disposition. Jerome was genetically engineered and phobias like acrophobia are not considered something that is inherent in our genes (or, at least, I have never heard of phobias being a genetic disposition). This is hinted at because at the end of the movie, before Vincent gives Lamar his real urine before the launch, Lamar says to Vincent that his son "wants to apply here [at Gattace]...Unfortunately, my son's not all that they promised". Notice the wording. There is nothing that suggests that Lamar's son had a failing because of his genes. In fact, it sounds as if it has come home to Lamar that parents can go to the geneticist to ensure their child has all the right genes (as Vincent narrates right at the beginning of the movie about Jerome before he admits that he in fact is not Jerome) and yet the rude awakening to Lamar is that "failings" in a person's humanity can actually occur from other factors beyond our genes, in this case, Jerome's fear of heights, hence why Jerome was not all that "they" promised. And who is this "they"? I think Lamar means the geneticists at the time Lamar and his wife chose the best "human potential" that later became their son. So, although Jerome had all the right genes to enable him to get into Gattaca, he had one failing that could not be linked to his genetic makeup (and hence a further poignant point to illustrate that our genes don't determine everything about our humanity). I understand that this is what Lamar was trying to say at the end of the movie about his son's set back. This is further accentuated when Jerome explains to Vincent about the silver medal and how Jerome was never meant to be second best. I can only guess that when he tried to get into Gattaca, he came out second best, that is, was rejected. I assume this based on the type of regimes prospective astronauts go through to test their stamina for space flight and therefore I guess that when Jerome had to do a test which included going to great heights, he refused to do so out of fear and hence this led to his rejection.
So, if Jerome was Lamar's son, I believe Lamar knew Vincent was imposing as Lamar's son right at the beginning. This is because, when Vincent had his "interview" and Lamar put the urine sample into the machine which revealed the true identity of the owner of the urine sample, Lamar had to know right from the beginning that Vincent was not Jerome Morrow - unless Lamar had not seen his son for many years and hence would not have been able to recognise him. But this is not suggested in the movie. Rather, the fact that Lamar tells Vincent that his son "admires" him suggests that this is a recent conversation between father and son, and hence possibly that Jerome had already given his father a tip off that someone else was going to be using his identity which would explain why Lamar was not surprised to discover that Vincent had Jerome's identity at that first interview. This then also explains why Lamar talks about his son and his son's admiration for Vincent right at the beginning and hence why it was not a surprise for Lamar to discover at the end that Vincent was in fact an In-Valid and yet Lamar was able to change the screen back to Jerome's particulars. This suggests that Lamar knew all along that Vincent was using Jerome's identity and hence had the capabilities to have an "ace up his sleeve" to revert the machine back to Jerome's identity should Vincent be in a compromising position. There is also the suggestion of collaboration between father and son, that is, that Jerome had told his father earlier on that Vincent was going to use his identity and hence wanted his father to do all he could to protect Vincent, not for Vincent's sake but for Jerome's. In other words, the motive behind Lamar doing what he did for Vincent was not because of Vincent but because Lamar loved his son, Jerome, and therefore assisted Jerome in fulfilling his dream through Vincent.
