You just need a video card that supports two monitors. Most do, and you don't need an expensive one for Lightroom - it doesn't make use of the graphics processor in the way games do (or Photoshop does).
A GEForce GT 610 is about £30 / $40, and is plenty powerful enough. Just make sure the card supports two monitors, with the connectors you need for your monitor (e.g. VGA, HDMI or DVI).
PS - are you sure your PC doesn't support two monitors already? Most I've seen since even Windows XP days have dual monitor support.