Malik Ishaq, who had been detained last week, was in a prison convoy in Punjab province when supporters opened fire in an attempt to free him, said police.
They said Ishaq was killed in a gun fight along with his two sons and 11 militants in Muzaffargarh district.
Lashkar-e-Jhangvi has been behind some of the most violent attacks on Shia Muslims in recent years.
Punjab Home Minister Shuja Khanzada confirmed the news to AFP news agency, while a doctor at Muzaffargarh District Hospital said 14 bodies had been received there.
Six police officers were also reported injured but correspondents say the details are unclear, and they have not been seen by the media.
Lashkar-e-Jhangvi was banned in Pakistan in 2001 and designated a terrorist group by the US in 2003.
The group is accused of killing hundreds of Shia Muslims in Pakistan.
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