Regarding the influence of this on the parliamentary election it should be noted that the Speaker Nabih Berri has
stated back in August that the idea of postponing the parliamentary election even further because of security concerns and the absence of a president is a no go.
The speaker has said that extending Parliament’s mandate beyond November would be futile given the utter paralysis in the legislative branch in light of a boycot by most Christian MPs and some March 14 lawmakers of all legislative sessions. The boycotting MPs argue that Parliament should only convene over urgent matters while the presidential seat is void.
Still, there is a genuine constitutional dispute over whether you can have a parliamentary election with no President elected.
Background:
https://now.mmedia.me/lb/en/Reports-Interviews/540670-complete-guide-to-lebanons-presidential-election