You would have the same approach lighting as you would without the displaced threshold, although the runway lighting itself might have some additional elements to it. It all depends on whether it is a starter extension (blue edge lights) or a stopway (red edge lights). This is if it is required to have lights though, which depends on what type of operation/weather minima the runway is used for.
One major point is that where you are required to have center line lights, and you have a displaced threshold usable for aircraft movement, the approach lighting is sufficient as far as center line goes up to the threshold.
(UK CAA CAP637) will give a very good overlook of the different lighting systems and their requirements.