I have come to the realisation that the chances of a TPK in the starter set are largely down to the actions the party decide to take.
I say this as a totally new DM after having run 3 2-3 hour sessions of LMoP for my wife and two kids (7 & 10) who have never played a session of DnD (or any other RPG) prior to this.
Having watched some various "play throughs" (WoTC, RollPlay one shot & few others I can't recall right now) and read some recaps (CMG Mark, MerricB and others) of the adventure I was worried how the kids would handle a PC death.
So what I did was buff their HPs up another hit die average (5 for a d8, etc.).
What happened instead was they acted as if they had been playing these types of games for years.
Not only did they not get dropped to 0 HP, the only one to even take any significant damage was the mute dwarf fighter DMPC who ran into melee for any fight he could find.
The PCs didn't even take any damage until the last room of the second set of encounters (trying not to cause any spoilers) when the cleric took a bite to the neck. That was it, a single hit against a PC in three sessions of level 1 play.
What they did was to continually move in stealth, look for ambushes and traps, interrogate (nicely if possible) every enemy they could capture, calm any animals they could and they were smart with how they went about combat (getting surprise rounds in on every encounter but the first, which they managed to mostly not get surprised by).
Surprise rounds a major factor in combat.
At least during the early levels, but I assume later as well.
It got to the point were I was questioning myself (new DM) as to whether I was being too nice to the PCs. But after going over how everything occurred I'm mostly just pretty proud with how they handled things.
tl;dr: "lethality" of the starter set is mostly set by whether Players decide to blunder into each encounter without thinking about stealth/traps/surprise/etc.