The British duo are on the lookout for a place to share near SW19, a cause which will be helped by the £78,000 they will have pocketed for their respective opening-round victories.
But the 24-year-old Gray was left to rue missed opportunities in a match in which Fritz always seemed a step ahead without having to raise his game.
The Briton hit a total of 30 unforced errors to 11 by Fritz, who had been knocked out by Gray’s former school friend Jack Draper – the pair having attended a school next to Chelsea’s Cobham training ground – at Queen’s earlier in the month.
Hopes that he could back up his day-two win against Tseng Chun-hsin were given some hope when he broke his American opponent in the second set and had the opportunity to serve for the set and level the match.
But he was broken, lost the subsequent tiebreak and then faltered in the final set to end what had been a promising Wimbledon debut.
More to follow