Unfortunately, Harry Fox does NOT handle Synchronization Licenses (for film and video), they handle only Mechanical Licenses (for sound recordings like CD's). Harry Fox gave it a try a few years ago, but since there is no statutory rate or even compulsory license for sync licenses in the USA, they quickly gave up as impossible.
But you can use their online Songfile database to look up who the copyright holder is. http://www.harryfox.com/public/songfile.jsp
It says that the owner of "Lux Aeterna" by Clint Mansell is...
UNIVERSAL MUSIC MGB SONGS OBO UNIVERSAL MGB PUB LTD
So you will have to deal with Universal to negotiate a sync license.
As Bob suggested, bring your checkbook. This is why there is a big business in "sound-alike" production music. Unless your client has deep pockets, you will likely be looking for similar production music.
Note that the licensing agencies like ASCAP, BMI, SESAC, handle things like broadcast and live performance rights. They don't handle mechanical licenses. You can use Harry Fox to get low-quantity (up to 2500) mechanical licenses, or you can go directly to the publisher/rights holder if you think you can strike a better deal than the statutory rate.
But if you want sync licenses, you must negotiate a separate deal with each publisher/rights holder. These have traditionally been high-$$$ deals, especially for well-known popular music.
Note that the sync licensing laws and practices vary dramatically in other legal venues. For example, in Canada, getting a sync license is almost as easy as getting a mechanical license from HFA.