We know that some characters have some level of plot armour as we play the game, but in real life, anything can happen. In life, there aren't any Season Twos to continue a character.
So, if you were Lee and knowing that Clementine will be without a protector after you're gone, which is just a few minutes away, would you do what the couple did in the mansion - putting a bullet in Clementine's head before putting one in your own?
I know it's disturbing to even think about doing that to a child, but the odds of Clem surviving are really low, unless she finds another protector like yourself, in a city of Walkers, with Vernon already out at sea, and Christa and Omid nowhere to be found.
Even assuming that you know that the Walker scent on her will offer her "invisibility" till she gets out of the city, any number of cruel things could happen to a little 9-year-old girl without a protector. She's still not ready to fend for herself yet, as she only just got rescued after being tricked into trusting Campman. She's really still just a naive little girl. Will you, out of compassion, end her life quickly and painlessly there and then?