No the Type S doesn't come with LSD.
IF you happen to find one cheap and you plan on changing clutch and such then it is worth while putting it in. What I did when I changed my clutch, made a hell of a difference.
Like I've said many times the real only major difference between a Type S and an Type R is the name and the LSD the Type R comes factory with. Everything else is really the same and not noticably different.
Also as Admant may have said the Type R may be 1/10 of a second faster but that 1/10 of a second will be more judged by the driver skill than the car itself. During my time in the Honda scene I've seen many Type S shit on Type Rs and vice versa in relatively standard modded cars with bolt ons, the major difference in these cases were the driver.