Yes, last hitting is an action, client input, just like any other, and any action has a delay. Not to mention the delay of any info getting to you in the first place, so lowering the ping increases your chance of response.
Plus ur not playing bots, so no 2 waves will be the same, and you have to react to any interaction your opponent creates with the wave. You also have to react to your own actions, as simply walking through them will make them try to walk around you and influence the rate at which the targeted minion's health is dropping. Not to mention certain abilities and items can change the speed and other attributes of both friendly minions and enemy minions...
And say u still stand still and all waves are the same, you will still not get everything the same every time, because packets differ and if that's not enough... They are sent at a certain tick rate which for one, shows the state of the game at certain times at fixed intervals (because this is not in real time and you don't get all the info all the time), and second, it entails windows of opportunity for the player to react. This can mean 2 things:
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imagine you need the minion at max health X to be able to last hit, and the server has these two states sent to you: first state with X+10 hp at say level 1-5, or 2*X hp at higher levels; and second state with 0 hp aka minion dead. The state in between is lost (why we sometimes see stuff teleport or just change more than it should in an instant, without freezes, cus thats another story) therefore the info you needed to react is just not there sometimes; it can also be drawn for a smooth experience, but lol doesnt have this interpolation thing. Mkk so lower ping cant fix this rare occurrence which actually makes the health drop rate inconsistent visually. But it can help with prediction accuracy (you get srv info sent to you faster, u have more time to react) and actual reaction time (the faster your input is received, the more impactful it is - minion might die if ur action is received too late) - btw this is all obvious stuff and should be enough
I think this unsmooth health drop rate matters less at higher levels cus u scale better than a minion, but when it does impact you, visually, your aa is seeing a cancel, minion died faster than anticipated (could also be poor anticipation ofc), or you could have the illusion of inconsistent champ dmg, suddenly higher at same level (noticeable if you do 2 or more hits per minion and suddenly, your 2nd to last hit turns into the fkn last hit) and/or in 1 instance simply lower at the next level, ofc making you miss the gold (could also be early therefore poor last hitting)
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a tiny fraction of a second might not seem to matter much, but when it comes to that window of opportunity to react, it only matters if it's within it. if it's right after, your action is rejected. might not matter if ur a few seconds early to catch the subway, but it sure matters if ur a few seconds late and the doors are closed in ur face. therefore input from players with a lower ping might not just be received faster (the old 'I died even tho I shot first'), but can also be the only input received at that tick, yours being completely ignored.
In minion terms, in the delayed case, you could have a shot go out but hit air cus minion dies in the meantime cus of bs delay. Visually, you hit something but no dmg shown, it died and u did not get the gold; if by mistake u clicked too early, ud see dmg done and minion die to enemy minion; if by mistake u clicked too late, ud see an animation cancel as minion dies, or your champ do nothing if minion already dead - pls correct me here if I'm wrong, because hitting air or smashing ground with an aa or targeted ability doesn't normally happen. In minion terms, in the ignored case, you can have that shot never sent (visually, ur champ does nothing and minion just dies and u go wtf I clicked it).
If you have lower ping, prolly lower than 50, and don't experience or visibly notice any of these abnormalities or inconsistencies, then lucky you. That doesn't mean they're not there for others.
Ignorance is bliss and you can always say na-ah, you just suck, but u can also read for yourself about how internet actually works, about protocols n packets, n how lag is a very broad definition and high latency is just one type of lag, and how it can affect games in particular, and how diff games are designed differently etc etc. And then come back with actual counter arguments proving I'm wrong partially or fully, or come to the same conclusion, lower ping is always better in pvp, for all input actions. And that includes farming, which is an important factor in the win percentage, that we can all agree on, and it's not by chance that win rate is influenced by ping.