Unity supports quite a lot of variations in lighting. You can do the normal point lights and spot lights, you can add light cookies (the little cutout shapes in lights) and shadows. In horror games they might also be using lots of what Unity calls "Sun Shafts", also known as "god rays" or "light beams" which can look amazing if you are trying to constrain what you see. It also supports layer-based blooms, crease shading, many kinds of light masks, and deferred lighting.

It is certainly possible that whatever specific feature he wants in his game may not be directly supported, but Unity provides many options out of the box.

There are already horror games out there made with Unity, so it's certainly 'right' for a horror game.

That, however, depends a lot on the mechanics of said horror game, and less on its theme.

As for the lighting in Unity, since it was mentioned in a few comments, the free version of Unity is really terrible with built-in lighting. Pretty much you're not going to get any decent lighting or shadow effects whatsoever, unless you can program them yourself essentially from scratch. The engine features for lighting are pretty much ALL restricted until you buy the pro version for $1500.

This can be detrimental to your game if you want to rely on lighting for effect. Though there are workarounds, of course, but it will be a huge pain and you'll have to know a lot about lighting.

However, you can still make a very creepy game without using the lighting effects. Personally I think the game Clock Tower on SNES is very creepy and it's made with bright 2D sprites. Into the Gloom on Desura is a really creepy game made in Unity's free version. Personally it scared me a lot. It doesn't use lighting effects to create atmosphere but is still very scary.The recently popular Five Nights at Freddy's game is completely 2D and used pre-rendered 3D stills (which you can make in something like Blender). The infamous Imscared was made in GameMaker, an engine designed for 2D, and doesn't use advanced lighting or anything to be scary, but rather some unique mechanics and 'story.' (The links are to YouTube plays of those games if you were curious to their gameplay).

In short, there are tons of examples that the engine is not what is important to make a horror game; it's all in the design.

Since you don't seem to have a very strict idea of what you're wanting to make right now, consider designing your game around a concept that won't need intricate lighting if you're using the free version of Unity, or if you really want to do some intricate lighting, look elsewhere or buy the pro version of Unity.

Horror games are all about the design and art. The engine has little to do with making a game "horror." You need to have good artwork, and good level design to induce those types of feelings. The only time the engine would come into play is if it limited you in one of those aspects.