Lerp in local space on moving object

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1

Hey,
how to lerp in local space when object is moving? This code work fine on static objects, but when it moves (fast) then cameraPart on start is a little bit far away to playerPart. I tried calculate offset on moving object and applied to initialCamera variable but this not work as expected.

Testing Code 
local TweenService = game:GetService("TweenService")
local RunService = game:GetService("RunService")

local playerPart = Instance.new("Part")
playerPart.Size = Vector3.new(3, 3, 3)
playerPart.Position = Vector3.new(0, 2, 0)
playerPart.Anchored = true
playerPart.Parent = workspace

local cameraPart = Instance.new("Part")
cameraPart.Size = Vector3.new(1, 1, 1)
cameraPart.Position = Vector3.new(-20, 10, 0)
cameraPart.Anchored = true
cameraPart.Parent = workspace

local increment = 1 / 360
local alpha = 0
local initialCamera = cameraPart.CFrame

while alpha < 1 do
	RunService.Heartbeat:Wait()

	playerPart.Position = playerPart.Position + Vector3.new(1.5, 0, 0)
	alpha = alpha + increment

	local cameraStartPosition = CFrame.new(playerPart.CFrame.Position) * CFrame.new(-5, 5, 0)
	local cameraFinishPosition = CFrame.new(cameraStartPosition.Position, playerPart.CFrame.Position)
	cameraPart.CFrame = initialCamera:Lerp(cameraFinishPosition, alpha)

	-- Refresh
	initialCamera = cameraPart.CFrame
end