Haroldas Bugaila, 29, shook 11-week-old Martinas Bugaila to death on 27 March 2019 after a row with his partner.
Lincoln Crown Court heard the youngster died after suffering a “catastrophic brain injury” akin to those seen after a “high-speed motor vehicle accident”.
Bugaila was ordered to serve a minimum of 23 years in prison.
Prosecutors said the defendant, formerly of Granville Street, Boston, had warned the children’s mother on more than one occasion that he would “make the boys cry” because she was speaking to him “in a way to which he objected”.
On the day of the murder, the court heard that after an argument with his partner, Aliona, the defendant had been left alone with Martinas and his twin brother for five minutes when he started to shout: “Come here, there’s something wrong.”
Jonas Hankin QC, prosecuting, told the jury “Aliona ran upstairs and looked in the cot. Martinas was on his back. He looked completely white. His eyes were closed and he wasn’t breathing.”
He said the infant was “turning blue” as his mother made resuscitation attempts.
“Martinas would have collapsed immediately or within seconds of being assaulted, such was the severity of his injury,” he added.
The court heard he was taken to hospital but died on 2 April.
Bugaila was found guilty of murder and of causing grievous bodily harm to Martinas between 5 February and 15 March 2019 following a six-week trial
He was also found guilty of two serious assaults on Martinas’ twin brother.
Det Supt Karl Whiffen, from the East Midlands Special Operations Unit, said: “The emotive nature of child death cases means that the investigation team, and in particular the two officers in the case, worked under a tremendous amount of pressure.
“Our sincerest hope is that the surviving twin will continue to recover.”