In "The Jedi", why did Lang the mercenary only fake a truce with the Mandalorian? Wasn't it really in his interest?

He wanted to avoid retribution from the population of the city and thought the Mandalorian might prevent his escape.

Lang was the lead strongman in a regime that had oppressed, tortured, and murdered many people in the city. He saw quite clearly that this regime he had been a part of was collapsing. The foot soldiers and droids had been defeated, and the leader was in a one-on-one battle with a Jedi that he did not think she would win (and even if she did, it would be two people against a whole city). He knew that soon, the city would be liberated and the people would be emboldened to seek justice against him, whether the Mandalorian alone honored the truce or not. He needed to make his getaway and he had a brief window where only the Mandalorian stood in the way of him doing so.

Having put my thoughts in writing, I now got something of an answer:

Lang assumed that the Mandalorian entered a truce with some people, but not with others and that he himself would be a corner case. Further either he assumed that Mando would eventually decide against him or he did not want to take his chances. So by offering a truce, he tried to pre-occupy Mando with pondering the offer to increase his chances in prevailing.

I find this just about plausible but not really satisfying, so any other answers are welcome.

It was a calculated gamble

Lang's actions are very much calculated to provide the biggest chance of his own survival. Let's take it step by step:

1. Lang faces Mandalorian: At the very beginning of this standout, Lang has two choices: ether start shooting or stall. He knows, that he has low chances of outright killing armed Manalorian. What he doesn't know, is the number and position of his troops and where is Ashoka (IIRC, the sounds of combat between Jedi and the Elsbeth start after the beginning of this standoff).
2. Ashoka fights with Elsbeth: Now Lang knows where his second enemy is. She still might lose and some survivors from his squad can come back. Shooting is risky, so is running away - stalling then is still the best possibility.
3. Ashoka wins: Now it is 2 vs 1, but the Jedi is still away. His soldiers are nowhere to be seen, so he needs to run. But, can he really trust Mandalorian to not shoot him in the back? How about any of the local population? How about the revenge of the angry Ashoka, who would see him as an accomplice to the tyrannical rule? His only option is to run away, find a nearest ship and fly off. It seems that the Razor Crest is the nearest ship and local people might think twice about shooting someone who managed to kill a mighty Mandalorian. So he takes a risk and tries shooting. He fails.