On 5 February 1934 Lübke was brought under investigation for corruption by the Nazis. He was arrested and after 20 months on 11 October 1935 released from custody.
Heinrich Lübke was one of the Presidents, who in his tenure did not sign any law that had been adopted by the Bundestag. After obtaining a scientific opinion he told the Bundestag president that he would not sign the law on operational and commercial staff, as it would violate his opinion against the constitution guaranteed freedom of choice of employment and vocational training.
At the official ceremony on 13 April 1972 Lübke’s merits were appreciated. Lübke was buried in Sunderland-Enkhausen after a Requiem in Cologne Cathedral. The family grave in the village cemetery in Enkhausen bears the inscription "Lübke - President from 1959 to 1969." In Sunderland-Enkhausen in 1975 the city museum, the Heinrich-Lübke-house, was furnished.