How do you make the mouse lock on to a HumanoidRootPart?

First of all, Mouse.Hit.p is a Vector3 value, and not a CFrame value. Mouse.Hit is already a CFrame value, so if you're trying to set the Mouse's CFrame, you don't need the .p at the end.

Mouse.Hit = Mouse.Target.Parent:WaitForChild("HumanoidRootPart").CFrame

However, you cannot change the Mouse's Position, as they're a readonly property. You can change Mouse.Target.Parent:WaitForChild("HumanoidRootPart").CFrame to the Mouse's CFrame (Mouse.Hit) like this:

Mouse.Target.Parent:WaitForChild("HumanoidRootPart").CFrame = Mouse.Hit

but like I said, you cannot set the Mouse's position to another position via a script.

Also, it is more safe and effient to get your own Character from the Player (Player.Character) , rather than getting it from the Workspace (game.Workspace:WaitForChild(Player.Name)).

If you want to Lock On to a Character's HumanoidRootPart, what I would do is make my own HumanoidRootPart to look at the opponent's HumanoidRootPart. Like this:

local Player = game.Players.LocalPlayer
local Character = Player.Character
local HumanoidRootPart = Character:WaitForChild("HumanoidRootPart")

local Mouse = Player:GetMouse()

local UIS = game:GetService("UserInputService")
local LockedOn = false

UIS.InputBegan:Connect(function(Input, gameProcessedEvent)
    if gameProcessedEvent then return end
    if Input.KeyCode == Enum.KeyCode.E then
        if LockedOn == false then
            LockedOn = true
            if Mouse.Target.Parent:WaitForChild("Humanoid") then
		local opponentsRootPart = Mouse.Target.Parent:WaitForChild("HumanoidRootPart")
                while LockedOn == true do
                    HumanoidRootPart.CFrame = CFrame.new(HumanoidRootPart.CFrame.p, Vector3.new(opponentsRootPart.CFrame.x, HumanoidRootPart.CFrame.y, opponentsRootPart.CFrame.z)
                    wait(0.1)
                end
            end
        elseif LockedOn == true then
            LockedOn = false
        end     
    end
end)

One more thing, using a while loop multiple times is not ideal. In this case, you should use a repeat loop, as it only loops until a certain condition.

From this:

 while LockedOn == true do
	HumanoidRootPart.CFrame = CFrame.new(HumanoidRootPart.CFrame.p, Vector3.new(opponentsRootPart.CFrame.x, HumanoidRootPart.CFrame.y, opponentsRootPart.CFrame.z)
	wait(0.1)
end

to this:

repeat wait(0.1)
	HumanoidRootPart.CFrame = CFrame.new(HumanoidRootPart.CFrame.p, Vector3.new(opponentsRootPart.CFrame.x, HumanoidRootPart.CFrame.y, opponentsRootPart.CFrame.z)
until LockOn == false

This will repeat its loop every 0.1 second until the LockOn value is false.

I hope I helped in any way, and I hope you find your best solution.