The biggest challenge with what you are trying to do is ensuring that both the input and output map projection parameters are set up correctly. The easting, northing, and central meridian of a sinusoidal projection tend to be highly customized to meet the needs of a particular data set and Lambert Conformal Conic is very sensitive when it comes to its origin, meridian, and parallels as well. You would likely have to research what the appropriate parameters are for Lambert in your region and set up a customized map projection to handle the conversion. You might also check to see if ENVI is reading the current sinusoidal projection correctly. You can do this by overlaying a basic georeferenced vector file of continents on your image. ENVI includes these under Vector->Create World Boundaries. If it is properly reading the file, you can also try spatially subsetting the large world file to an area that just covers what you need, then try the map conversion again.