John Lithgow did not receive an Oscar nomination for portraying Burke in Blow Out.
John Lithgow portrays Burke the mystery hit man who causes the titular blow out to occur which kills a politician who threatened to take the party nomination from the current president. Burke is a strange man, and if you want someone strange well John Lithgow certainly can fit the bill. Burke is a most bizarre hit man who, like Frank in Once Upon a Time in the West, disobeys his bosses orders and kills feeling his bosses measures were not extreme enough to get the task done. Burke then goes on to take just as extreme of measures to cover up what happened the night the politician died, which actually goes beyond destroying the evidence and even killing the witnesses.
Burke, to make the cover up airtight, does not want to just kill the one of the main witnesses, but rather desires to create a serial killer to make it seem like she was merely one of the many people he murdered. This puts Burke as most oddly intriguing character which is a trained "sane" killer who pretends to be a more run of the mill psychopath. Lithgow plays this strange game very well with his performance that comes in out of the film as Burke basically builds his manufactured serial killer until he thinks it is time to finish the cover up. Lithgow is interesting because on the surface he makes Burke a man who is doing his job, and acts just as a man doing his job. He doesn't really take pleasures in the murders, but does them because he feels they are needed.
Lithgow is very effective in showing the way Burke creates the killer as an act. Up to the killing he portrays the stalker psychopath after his prey, but actually doing the killing itself Lithgow almost looks like he taking out the trash, as for Burke it is just part of his plan. After the murders Lithgow plays a part upon a part as Burke calls the police to fake a serial killer identity, making his serial killer some sort of deranged hill billy. Lithgow has the right efficiency in his portrayal of this with him being a completely believable psychopath as he informs the police, but as soon as he is ending the call Lithgow instantly returns to what Burke is which is trained fixer who does not have the emotional attachments like his false serial personality he has manufactured.
This is a very well handled turn by John Lithgow. Lithgow in a way is kind of a secondary lead, only kind of as it definitely is not Burke's story, because the film does allow us to see the whole implementation of Burke's plan to cover up the murder that coincides with Travolta's character's attempt to try to uncover it. Lithgow slowly builds up the menace of Burke slowly in his scenes that come in and out of the film until the point in which he finally decides to proceed with the target. The end of the film is an incredible tense sequence only made more so because of the way Lithgow has made Burke a properly chilling figure that makes his mere appearance something to fear.