According to police, advocate Malik Saleem Latif and his son advocate Farhan were going to court in Nankana Sahib, some 80 kilometres from Lahore, when unidentified men opened fire on them, killing Saleem on the spot while injuring Farhan.
Farhan was taken to local hospital where his condition was stated to be critical.
Saleem was the cousin of Nobel laureate scientist Abdus Salam. He was president of Jamaat-e-Ahmadiya Nankana Sahib.
LeJ Al Alami, a faction of the Lashkar-e-Jhangvi, has ties to the Taliban, al-Qaeda and most recently Islamic State militants. The group has been behind major terror attacks in Pakistan, including last month's suicide bombing of a Sufi shrine in Sindh province that killed more than 90 people.
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LeJ was founded in 1996 as a militant offshoot of Sipah-i-Sahaba, a Sunni sectarian group that emerged in the mid-1980s. LeJ has claimed responsibility for the deaths of hundreds of civilians, mostly minority Shia Muslims.
"Advocate Saleem has been targeted purely for his faith and the government has failed to rein in those elements spreading hate openly against the Ahmadi community," he said and demanded immediate arrest of the culprits.
The killing of Saleem puts the spotlight back on Pakistan's problem of Ahmadi persecution. The issue is deep-rooted and dates back to pre-Partition of India.
In 2014, 11 Pakistani members of the Ahmadi community were reportedly murdered. At least six Ahmadis were killed in Pakistan in 2016 for their religious beliefs.
In 1984, Ahmadis were restricted from "misusing" the epithets, descriptions, titles reserved for certain holy personages or places of Islamic origins. They could not call themselves Muslim or propagate their faith.