In a statement on its Twitter account, picked up by the private terrorism watchdog SITE, the group posted a photograph that it said showed soldier Ali al-Bazaal's execution.
"If the sisters that were unjustly arrested are not released, then after a short period of time the death sentence will be executed against another prisoner we hold," it declared.
The group did not identify the women and children it said Lebanon is holding, nor did it say how many were missing.
Signup to our newsletter and follow us on Facebook and Twitter!
On Wednesday, Lebanon's interior minister said authorities there were holding the daughter and former wife of Abu Bakr al-Baghdadi, who leads the Islamic State jihadist group, a rival of Al-Nusra.
While both based in neighboring Syria, Al Nusra and the Islamic State have clashed with Lebanese border forces and with the Lebanese militia Hezbollah, which supports Syrian leader Bashar al-Assad's regime.
Last month a roadside bomb wounded three Lebanese soldiers near Arsal, where in August troops fought a fierce gun battle with jihadists who streamed across the border.
Fighting ended with a truce mediated by clerics, but the jihadists took with them 30 Lebanese army and police hostages.
At least four have since been executed, and Qatari-led efforts to free the rest have so far yielded no concrete result.