Yes, you remain invisible.
The text states:
When you are in an area of dim light or darkness, you can use your action to become invisible until you move or take an action or a reaction.
We can break it up to determine how it works.
When you are in an area of dim light or darkness, you can use your action to become invisible
This is the only condition that must be met for you to become invisible. If you are in dim light or darkness, and you can take an action, you can become invisible full stop.
until you move or take an action or a reaction.
These are the only conditions that cause you to lose invisibility. The invisibility ends when you either move, take an action, or take a reaction. Transitioning from dim light/darkness to full light is not moving, taking an action, or a reaction, so the invisibility remains.
If you're worried about this being overpowered, remember that in 5E invisibility is not that useful by itself. It doesn't actually make you any stealthier or harder to detect than normal. The only thing it does is give people disadvantage against you (which is powerful no doubt), and it allows you to hide in plain sight. However, hiding is an action, which according to the text you quoted removes the invisibility. Since your Warlock can't hide without losing his invisibility, he will still be detectable by everyone around him. All this lets your Warlock do is get disadvantage on attacks against him as long as he doesn't move or take actions/reactions.