onPlayer Added morph?

The code you posted has a syntax error, because there's a random function definition on the third line. Get rid of that to begin with.

hit is never defined -- before, it was from the part contacting the button.

You want to get the player's Character if you're doing things like looking for a Humanoid.

You could just use player.Character, but that will only work the first time they spawn. You want to use the .CharacterAdded event.

In any case, it's easier to make a function which dresses up a given character:

function morph(character)
    local g = game.Lighting.Morph1.Arm1:clone()
    g.Parent = character
    local C = g:GetChildren()
    for i=1, #C do
        if C[i].className == "Part" then
            local W = Instance.new("Weld")
            W.Part0 = g.Middle
            W.Part1 = C[i]
            local CJ = CFrame.new(g.Middle.Position)
            local C0 = g.Middle.CFrame:inverse()*CJ
            local C1 = C[i].CFrame:inverse()*CJ
            W.C0 = C0
            W.C1 = C1
            W.Parent = g.Middle
        end
        local Y = Instance.new("Weld")
        Y.Part0 = character["Left Arm"]
        Y.Part1 = g.Middle
        Y.C0 = CFrame.new(0, 0, 0)
        Y.Parent = Y.Part0
    end

    local h = g:GetChildren()
    for i = 1, #h do
        if h[i].className == "Part" then
            h[i].Anchored = false
            h[i].CanCollide = false
        end
    end
end

Now we can just make morph happen whenever a character spawns using the CharacterAdded event. To be safe, we might want to call it on their original character, too, in case we weren't quick enough.

function onPlayerAdded(player)
    player.CharacterAdded:connect( morph )
    if player.Character then
        morph(player.Character)
    end
end
game:GetService("Players").PlayerAdded:connect( onPlayerAdded )

You can simplify your morph function a little. For instance, C and h are the same thing. You should use :IsA("BasePart") rather than .className == "Part". You should also use good variable names! What about g describes that it's an arm part being added to the player? What about h suggests it's pieces of the arm?

You also add new weld to the left arm for each part in the arm, but it's only attached to one. Either that should be using, e.g., C[i] instead of g.Middle, or you should just do it after (or before) the loop.

You can make slightly more readable code using generic for loops, too, by avoiding all of the [i]:

function morph(character)
    local newArm = game.Lighting.Morph1.Arm1:clone()
    newArm.Parent = character
    for _, child in pairs(newArm:GetChildren()) do
        if child:IsA("BasePart") then
            local W = Instance.new("Weld")
            W.Part0 = newArm.Middle
            W.Part1 = child
            local CJ = CFrame.new(newArm.Middle.Position)
            local C0 = newArm.Middle.CFrame:inverse()*CJ
            local C1 = child.CFrame:inverse() * CJ
            W.C0 = C0
            W.C1 = C1
            W.Parent = newArm.Middle
            --
            child.Anchored = false
            child.CanCollide = false
        end
    end
    local Y = Instance.new("Weld")
    Y.Part0 = character["Left Arm"]
    Y.Part1 = newArm.Middle
    Y.C0 = CFrame.new(0, 0, 0)
    Y.Parent = Y.Part0
end