The case against JuD was brought by a real estate agent, Khalid Saeed, who says the charity had summoned him in January to appear at its court in Lahore to resolve a property dispute with another man.
Saeed told Reuters that the JuD letter warned him if he failed to attend, "no excuse would be accepted and action will be taken according to sharia".
The judiciary has become increasingly assertive dealing with politicians, but the case could show how ready judges are to act against powerful Islamic organisations.
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LHC Judge Shahid Bilal Hassan agreed to hear the case on Tuesday. He reserved judgment until a later date but told JuD's lawyer that based "on facts, he (Khalid Saeed) has a point".
There was no hearing on Wednesday and it was unclear when the proceedings would continue.
Court documents show the group is accused of organising and holding parallel sharia courts, summoning individuals and deciding family, civil and criminal law cases in Lahore.
JuD officials deny having links to LeT or running a parallel court system. Instead, JuD said it holds "arbitration councils" chaired by religious scholars who mediate disputes and provide guidance in light of Islamic teachings.
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During Tuesday's hearing the JuD lawyer, Muhammad Aqeel, said the summons submitted by Saeed was forged.
A JuD representative, Nadeem Awan, also told Reuters the group does not issue threats or summons.
"If we had been summoning people or coercing them to attend the council or abide by the council's decisions, then there would be thousands of complaints against us," Awan said. "Yet, all you have is this one complaint."
Many people are frustrated with the formal judicial system, regarding it as flawed and slow, and they instead look for justice from parallel courts like panchayats, or village councils, or unauthorised sharia courts.
The man who asked the JuD to intervene in his dispute with the real estate agent said he had written to the group's leader asking for help.
"A friend told me about these courts and how effective they are," Muhammad Azam told Reuters.
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