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By the end of S01E07 of Star Trek: Discovery, Mudd knew a lot about the Spore Drive. Also, Starfleet had every right to imprison Mudd as he committed serious crimes against Federation.
Why did Captain Lorca let him go free which could be costly? Mudd could sell those secret information to Klingons or he could attack Discovery or Federation again with his criminal mind.
Regarding the “secret information”: the Klingons were already aware of the Discovery and it’s abilities. So it whether it was “secret” and the Klingons would want to buy it is questionable.
However, Mudd never found out what the secret to the Discovery was. He knew it had a special engine, but that’s all. The best deal he could make would be delivering the Discovery to the Klingons, which he failed to do.
The other tradeable information Mudd gained was primarily access codes to the Discovery’s computer systems - security codes which could (and would) be changed - and what was in Lorca’s psycho man-cave.
As for Lorca’s motives:
Lorca is from the Mirror Universe, which is revealed after the Mudd incident, so the security of the Federation, let alone whether the Klingon Empire wins, would not be something that he cares about.
Also, Federation “prisons” in the Trek universe, are like “recreation resorts,” according to Kirk. They focus on reform. What happened to Mudd was definitely a punishment,
given how much he hates Stella, her father and how restricted his actions would be, by being a stay-at-home husband.
In Universe its very inconsistent with Lorca's behaviour. Out of Universe they needed to leave Mudd in one piece so he can show up in Kirk's time, and somehow be a very different character.
The plan to thwart Mudd was very specific: they needed a ship in close range that they could "redirect" Mudd's signal to (from the captain's chair). They also needed a ship that get the signal and show up quickly (like the Klingons would).
Perhaps no friendly ships were in range, or perhaps they were thought a friendly ship wouldn't care about weird message from a "Harry Mudd", and would just ignore it. Whatever the reason, they decided the most reliable target for the signal would be Stella and her father. Obviously, they chose right, because Stella and dad showed arrived just as expected, and took Mudd away, just like they wanted.
Part of your question is why Captain Lorca would allow Mudd to simply leave.
As a Starfleet officer, he simply couldn't justify executing Mudd. And once Stella and her dad arrived to take Mudd away, it would have been very unappreciative, and potentially dangerous, to execute Mudd (since Mudd was the only reason Stella and dad came in the first place).
If you've seen the whole season:
We eventually learn that Lorca is from an alternate universe, and isn't truly a member of Starfleet, but of the Terran Empire. He definitely doesn't have moral objections to killing Mudd.
But - his entire plan depends on his ability to maintain his cover as the "in-universe" Gabriel Lorca. If he had killed Mudd or destroyed Stella's ship, he would have seriously jeopardized his cover.
