Alistair Conall Hamish Lethbridge-Stewart

Alistair Lethbridge-Stewart was a member of the Lethbridge-Stewart family, he had a brother called Archibald, and was the paternal grandfather of Brigadier Alistair Gordon Lethbridge-Stewart, who was named after him. He was married to Lillian McDougal, and they had two sons, Matthew Lethbridge-Stewart, and Gordon Conall Lethbridge-Stewart, who was born in 1902. (PROSE: The Wages of Sin, The Forgotten Son, Night of the Intelligence)

During World War I, he worked British Intelligence in Russia but was forced to return to the United Kingdom in the aftermath of the Russian Revolution of 1917. One of his colleagues was Bertie Stopford, the then British ambassador to Russia. At that time his brother served as a captain in the Royal Artillery, and had two sons. (PROSE: The Wages of Sin)

He became a grandfather in 1925 to James Lethbridge-Stewart and again to his namesake, Alistair Gordon Lethbridge-Stewart, in 1929. (PROSE: The Forgotten Son)

Another account said that he became a grandfather when Alistair was born in India in 1930. (PROSE: Blood Heat, Island of Death)

Lethbridge-Stewart frequently pressurised the younger Alistair into following his footsteps and joining the British military. For Christmas 1938, he gave Alistair a box of toy soldiers and then asked him, "What do you want to be when you grow up?" Alistair was not pleased with his present. (COMIC: The Warkeeper's Crown)

On his deathbed, he told a commissioned Alistair that he was proud of him. (COMIC: The Warkeeper's Crown)

Behind the scenes
As confirmed by Mark Gatiss, the character of Archibald Hamish Lethbridge-Stewart, whom he portrayed in TV: Twice Upon a Time was intended to be the grandfather of Alistair Gordon Lethbridge-Stewart. However, the episode itself does not explicitly state their relations.

However, on both Twitter and Facebook, the Creative Director of the Haisman Estate, copyright owners of the Lethbridge-Stewart IP, made it clear that neither the Haisman Estate nor Henry Lincoln consider the character the grandfather, but rather the grandfather's brother.