This is not accurate, though the logic does seem to make a little sense. If you lifted hard and with any significant volume, the fatty acids released (the small amount that is) will be used primarily for meeting increased energy needs you've created by lifting. Remember that caloric expenditure doesn't end when you put the weight back on the rack.
Your best method (to the original poster) is to use High Intensity Interval training (basically a bunch of sprints) on days seperate, or at least 5 hours removed from, lifting. Say, lift MWF in a maintainance program while doing sprints (or calisthenic complexes, something of the sort) T/Th/Sat
The exact number of days and intensity levels/volume will depend on a lot of personal factors - pay attention to what your body is telling you and get your diet in order and you'll do well.