Many filtered CCD measures form the basis of six new light curves of the eclipsing system SW Lyn. From these measures and additional observations for eclipse timing, 47 new times of minimum light over the time-interval of about 13 years have been calculated. The complex period variability can be sorted into a linear period improvement with 5.8-year and 33.9-year periodic terms. The shorter cyclic term of these is ascribed to a cool companion of the eclipsing pair but the longer one has no testable interpretation at present. The new light curves are synthesized by the 2003 version of the Wilson-Devinney differential corrections computer code. The results incorporate a source of "third light" which comes from the cool companion star that had been identified by the cycling of the period of the eclipsing pair and also had previously been identified spectroscopically. There is a measure of satisfaction with current understanding of the SW Lyn eclipsing system because of consistent syntheses of all historical light curves. This agreeable convergence, however, comes partly at the expense of an unanticipated temperature of the hot star and of a photospheric spot that has no obvious basis in the detached character modeled for the binary. We offer predictions of changes in the stellar parameters if the modeled detached-configuration should be wrong. The SW Lyn stellar system is still difficult to understand.