How can I edit this script to make it R15 compatible?

Try this?

wait(1)
User = game.Players.LocalPlayer
Humanoid = User.Character.Humanoid
Torso = User.Character.UpperTorso or User.Character.Torso -- If not UpperTorso then It will do Torso for R6 instead of R15
L_Hip = Torso["Left Hip"]
R_Hip = Torso["Right Hip"]

function ArcTan(x, y)
    r = math.atan(y / x)
if x < 0 then
    r = r + math.pi
end
return r
end

vel = Vector3.new()
while true do
    wait()
    if Torso.Velocity.magnitude > 1 then
        m = (vel - Torso.Velocity).magnitude / Humanoid.WalkSpeed
        vel = (Torso.Velocity * m + vel * 2) / (m + 2)
        v = Torso.CFrame:pointToObjectSpace(vel + Torso.Position)
        L_a = ArcTan(v.x, -v.z)
        R_a = 3.1416 - ArcTan(v.x, v.z)
        L_Hip.C1 = CFrame.new(0, 1, 0)*CFrame.Angles(0, L_a, 0)
        R_Hip.C1 = CFrame.new(0, 1, 0)*CFrame.Angles(0, R_a, 0)
        L_Hip.C0 = CFrame.new(-0.5, -1, 0)*CFrame.Angles(0, L_a, 0)
        R_Hip.C0 = CFrame.new(0.5, -1, 0)*CFrame.Angles(0, R_a, 0)
        L_Hip.MaxVelocity = Torso.Velocity.magnitude / 100
        R_Hip.MaxVelocity = Torso.Velocity.magnitude / 100
    else
        L_Hip.C1 = CFrame.new(0, 1, 0)*CFrame.Angles(0, -1.57, 0)
        R_Hip.C1 = CFrame.new(0, 1, 0)*CFrame.Angles(0, 1.57, 0)
        L_Hip.C0 = CFrame.new(-0.5, -1, 0)*CFrame.Angles(0, -1.57, 0)
        R_Hip.C0 = CFrame.new(0.5, -1, 0)*CFrame.Angles(0, 1.57, 0)
    end
end

You need to define the correct limbs and joints for each rig type to make it compatible.

...
Torso = User.Character.HumanoidRootPart
if Humanoid.RigType = Enum.HumanoidRigType.R15 then
    L_Hip = User.Character.LeftUpperLeg.LeftHip
    R_Hip = User.Character.RightUpperLeg.RightHip
else
    L_Hip = Torso["Left Hip"]
    R_Hip = Torso["Right Hip"]
end
...

Edit: Use HumanoidRootPart instead of LowerTorso