It is possible that Voldemort already knew about The Mirror of Erised and told Quirrell to bring Harry in front of mirror based on logic. But, how did he find out that Harry was lying, and more importantly, that the Philosopher's Stone was in his pocket?
It all matters about Legilimency. Voldemort was highly skilled in the art of Legilimency.
Here is a quote of Harry Potter Wiki:
"Voldemort has used Legilimency extensively, both wandlessly and nonverbally, to enter the minds of those he wished to interrogate."
The quote can be found here, under History, third paragraph, first line.
This shows that Voldemort knew what he was doing because of his extensive knowledge, and this quote shows his skill:
"You flatter me," said Dumbledore calmly. "Voldemort had powers I will never have."
Voldemort was a very intelligent wizard.
To get to your question, here is another quote found on the Harry Potter Wiki:
"If a target is not skilled in Occlumency, a Legilimens will be able to detect if the person is lying, as well as delve into their thoughts, emotions, and memories."
The quote can be found here, under Methods, first paragraph, second line.
Harry was not even aware of Occlumency and Legilimency, so obviously he would be "bad" at it. This was evidently shown during, and after the fifth book, during, and after his lessons with Snape. Voldemort could have detected, through Quirrell that Harry was lying, and furthermore "delved into his thoughts", and saw that has was thinking about the stone in his pocket.
This is purely speculation.
Harry had been clutching his pocket from the moment the stone appeared in it. All Voldemort had to do was look at him and read his body language well enough, and apparently he did.
It should also be noted that Voldemort had a mental link to Harry's mind, which may have let him more easily read what Harry was thinking.