Note: edited this many times, I'd appreciate double checking from someone better at math than me.
As Greed mentioned it's not just the earlier Lead Shot that you overwrite, but also also the opportunity cost involved in using the buff to fire an extra Lead Shot (i.e the opportunity cost of not using that buffed GCD to fire something else like Split Shot). Given that our primary weaponskills are Split, Slug, and Clean Shots which are 140, 180, and 200 potency respectively, let's say that on average a GCD spent casting one of them is worth 173 potency. (Actually slightly more since sometimes we fire them with ammo which adds 20 potency, but let's ignore that to make it easier).
Visualizing the opportunity cost is a bit more difficult that I thought, since even though reapplying Lead Shot early is a GCD that you spend not casting a 1-2-3 weaponskill, if you look at the big picture it means that when someone who didn't refresh early is reapplying Lead Shot later, yours is still ticking and you get to fire a 1-2-3 weaponskill. So the opportunity cost is not the whole potency value of that weaponskill (173 * x), but only the additional damage on that weaponskill due to the buff ((173 * x) - 173).
Example 1.
Assuming a 10% buff, opportunity cost is 17 potency:
A 10% buffed Lead Shot is only 49 extra potency, if you clip 1 dot tick (3s left) you lose 45 potency, so even in the best case where you only clip 1 tick, it's still a DPS loss (45 + 17 > 49).
Example 2.
Assuming a 50% buff, opportunity cost is 87 potency:
A 50% buffed Lead Shot is worth 245 extra potency, 245 - 87 is 158, that's 3 ticks. If Lead Shot has 9s or less remaining, it's a DPS increase.
Example 3.
Assuming a 100% buff, opportunity cost is 173 potency:
A 100% buffed Lead Shot is worth 490 extra potency, 490 - 173 is 317, that's 7 ticks. If Lead Shot has 21s or less remaining, it's a DPS increase.
Fun fact, if you gain a 155% damage buff, overwriting a normal Lead Shot is always a DPS increase, even if your last GCD was also Lead Shot (meaning you waste the whole thing). The reason it gradually gets better to overwrite unbuffed Lead Shots at stronger and stronger levels of buffs is because it's relatively stronger than the average weaponskill (490 vs 173), but as you can see it would need a level of buff that is pretty unfeasible in practice. This is pretty much getting into boss mechanics territory for things to take that much extra damage, still good to know though!
So, given the strength of player buffs it's basically almost never worth it to reapply Lead Shot just for that - and that's not even getting into the problems you'll cause for yourself by unsyncing your Hot Shot and Lead Shot timers from each other.