Help with :Lerp() please?

It looks like you want the brick to teleport halfway between its current CFrame and ApproachingPart's CFrame when a player touches it.

All that Start:Lerp(Destination, Percent) does is return a CFrame that is linearly interpolated between two points. Start is the CFrame you start with, Destination is the CFrame you want to end with, and Percent describes how much you want to tween in (e.g. setting Percent to 0.50 will return a CFrame that is halfway (50%) between Start and Destination. Setting Percent to 1.00 will effectively return Destination (100%)).

In your script, all you forgot to do is make the CFrame of the part equal to the value to got from :Lerp.

script.Parent.Touched:connect(function(part)
    print("Lerping")
    local humanoid = part.Parent:WaitForChild("Humanoid")
    if humanoid then
          script.Parent.CFrame = script.Parent.CFrame:lerp(script.Parent.Parent.ApproachingPart.CFrame, .5) -- set the parts CFrame to what you got from :Lerp()
    end
end)

However, this is just one way of using :Lerp. What :Lerp is really useful for is making smooth transitions between two CFrames. To make the part smoothly transition between its current position and ApproachingPart's position, do this:

-- it is very good practice to store variables when you expect to use them frequently.
-- it's also less clutter on the script.
local startpart = script.Parent
local approachingpart = game.Workspace.ApproachingPart

-- the CFrame the part started with
local startcf = startpart.CFrame
-- the CFrame you want the part to end with
local endcf = approachingpart.CFrame

startpart.Touched:connect(function(part)
    local humanoid = part.Parent:WaitForChild("Humanoid")
    if humanoid then
        print("Lerping") -- this should probably be inside the if-statement
        for per = 0.00, 1.00, wait() do -- from 0% to 100% of the way, do...
            startpart.CFrame = startcf:lerp(endcf, per)
            wait()
        end
    end
end)