Character Parts Are Returning As Nil?

I think i have fixed your problem, first I removed the first table becuase, it was not needed at all. Second, I made a remote event called Lift and let it in ReplicatedStorage moving the script to ServerScriptService.

The for loop was receiving the info from the first list so you were declaring :GetChildren() more times than needed, also :GetChildren() returns a table so you cannot just do part:GetChildren().Name, you first need to make a for look and then print the name of each table values

Im not sure but I think Player.Character:GetChildren() Was returning nil cause as .Character simulates the character it is not getting the real info from the real one. So what I did was a

workspace:FindFirstChild(Player.Name)

doing that and then using :GetChildren() worked

Also .ClassName() i dont think its used I mostly use :IsA() but btw here the fix

game.ReplicatedStorage.Lift.OnServerEvent:Connect(function(Player)
    --local list = {"Head","LeftFoot","LeftHand","LeftLowerArm","LeftUpperArm","LeftLowerLeg","LeftUpperLeg","LowerTorso","RightFoot","RightHand","RightLowerArm","RightLowerLeg","RightUpperArm","RightUpperLeg","UpperTorso","HumanoidRootPart"}
    Player.leaderstats.Strength.Value = Player.leaderstats.Strength.Value + 1
    Player.Character.Humanoid.WalkSpeed = 0
    Player.Character.Humanoid.JumpPower = 0
    ----Modified by le145
	local PlayerWork = workspace:FindFirstChild(Player.Name)
	local allParts = PlayerWork:GetChildren()
	for i,v in pairs(allParts)do
		if v:IsA("MeshPart") then
			v.Size = v.Size+v.Size/200
		elseif v.Name == "Head" then
			v.Mesh.Scale = v.Mesh.Scale+v.Mesh.Scale/200
		elseif v:IsA("Accessory")then
			local mes = v.Handle
			if mes then
				local hand = mes:FindFirstChild("SpecialMesh") or mes:FindFirstChild("Mesh")
				hand.Scale = hand.Scale+hand.Scale/200
			end
		end
	end
	----------------------------------
    wait(.5)
    Player.Character.Humanoid.WalkSpeed = 16
    Player.Character.Humanoid.JumpPower = 50
end)