The name above the door is probably the licensee,
a Mrs Weston who was there for many years.
The Weston Suite, in the 80's, was where they had wedding receptions.
Apparently, her ghost is said to haunt The Dun Cow Inn??

..

It was built in the 16th century as a yeoman’s house but soon became an inn called over the years ‘The Lion’, ‘The Red Lion’ and ‘The Falconer’. At one time it had a grocer’s shop facing onto the main road. It ceased to be licensed in the late 19th century and became a farmhouse. There is said to be a tunnel containing a small room that runs from the cellar under the road to near the ‘Green Man’. The Home Guard had their headquarters here during the 2nd World War and the English Electric Company acquired it in 1954. Source: A Glimpse into the Past by Freda Bennett, 2006.

The old Lion Inn where the gunpowder Plot conspirators met on fifth November, 1605 to await news of the destruction of Westminster. Upon the arrest of Guy Fawkes their plan to seize Princess Elizabeth from nearby Coombe Abbey was abandoned and the rebellion which led to their defeat three days after the fifth was planned by the conspirators here at the Lion. 
In 1605 the monarch was James I; the Princess Elizabeth was his eldest daughter and sister to the future Charles I. In 1605 she was nine and being educated by Lord Harington at nearby Coombe Abbey. She wasn’t a Catholic, but the conspirators planned to convert her and use her as their figurehead. 

This is Frank Clarke Smith and his pet monkey Ginny. He was the landlord of the Green Man in Dunchurch in the 1920s when the photo was taken. The really eagle eyed might notice this photo is taken in the garden of The Green Man public house. Frank is the grandfather of Nicholas Smith, who lives in Rugby, and Frank was born in 1882 and died in 1956, 14 years before Nicholas was born. Nicholas married the sister of the current landlord of The Green Man  (now 2020), who has been landlord for the last 15 years. This is almost a hundred years after his grandfather Frank Smith had left. Nicholas' father is still around and confirmed the landlord's memories.

2019

We've previously mentioned the bomb falling on Dunchurch Working Men's Club on November 19, 1940, when June Williams - who was ten at the time - was recounting her memories of that fateful evening. Her parents were the steward and stewardess of the club. Two men playing billiards were killed that night, ironically having come over from Coventry to miss the blitz.

Fortunately for June's family, the bomb fell at 8pm, so she, her sister Cynthia and their evacuee were in the back of the building. Her father had been outside getting wood for the fire and saw the bomb coming down so told them to dive under the table. Unfortunately her mother, Kathleen Wilson, who was serving in the bar, was buried for a couple of hours and ended up in plaster from her hip to her knee. June would love to know who the boy in the picture is? She's also not sure if the white box is a phone box, or perhaps an RAC box