Can I fly a "Contact Approach" to this airport? In order to request and receive a clearance to conduct a "Contact Approach" the airport, among other requirements, must have a published instrument approach (IAP) and be reporting at least 1 mile visibility.  

If the visibility being reported for this airport (Lake Tahoe -TVL)  is 2 miles, and thus below minimums for any IAP, would it be legal to conduct a "Contact Approach?" 

(The two IAPs shown below are the only published approaches and the plates have been trimmed for brevity.)
Here are the requirements for a contact approach from the AIM 5-4-25:


  Pilots operating in accordance with an IFR flight plan, provided they
  are clear of clouds and have at least 1 mile flight visibility and can
  reasonably expect to continue to the destination airport in those
  conditions, may request ATC authorization for a contact approach.


If all those things are true then you can request a contact approach (ATC can't offer it). But ATC has requirements to meet too:


  Controllers may authorize a contact approach provided:  
  
  
  The contact approach is specifically requested by the pilot. ATC cannot initiate this approach. EXAMPLE− Request contact approach.
  The reported ground visibility at the destination airport is at least 1 statute mile.
  The contact approach will be made to an airport having a standard or special instrument approach procedure.
  Approved separation is applied between aircraft so cleared and between these aircraft and other IFR or special VFR aircraft.
  


If those things are also true then ATC can authorize it but there's no guarantee that they actually will.

In the example you gave, it looks to me like all the requirements are indeed met (although you didn't say whether the two-mile visibility is flight, ground, or both), so a contact approach would be legal. There's no requirement to comply with the minimums for a published approach during a contact approach.