Are there any LSA aircraft that can be flown IFR in IMC?
Sorry to reanimate this rather old question, but I'm surprised none of the previous answers mentioned the Evector SportStar MAX, which has a model that is IFR equipped and which was available several years before this question was asked. From its POH (section 1.2):


  Certification basis
  
  SportStar MAX complies with the ASTM F2245-07a Standard Specification for Design and Performance of a Light Sport Airplane, issued by ASTM International Committee F37.
  
  IFR version complies with FAR 91.205 requirements, ...


Here's a Plane &amp; Pilot review of the IFR version, and here's a Press Release from Evector about this model.

Evektor followed the MAX model with the Harmony, and at least one place on their website suggests it too is available in an IFR equipped version.