Absolutely, saves wear on tyres to start. No more wheels spins from the pull away especially in the wet. No more back end breakaway in fast corners, coupled to Avon CRZZ6 tyres of course.
Before we all get euphoric about LSDs there are few points to consider:
1 The MMC "standard" in the Dana Spicer axle is the friction clutch type, and is quite susceptible to begin set up wrong from the start. Some versions need a special additive in the oil.
2 The Quaife torque biasing diff recommended by Tim (which I fully endorse BTW) is a much better option for most applications and Morgans in particular.
3 The LSD will promote understeer at most times when used with a gentle throttle, this might detract from your enthusiastic driving but it is the "safe" option
4 When you reach the point at which you do break traction , now both rear wheels will be spinning, and you had better be used to this , and good at catching it. If you are , and can , then there is no doubt that an LSD is a great addition to your car and will enhance your Morgan driving experience.
I summary think about what you want from your Morgan and how you drive it. If you regularly go off road then an LSD provides much needed traction, if you compete with the car then it gives far superior traction out of corners, but if you just want to tour around (at legal speeds?) and are a fair weather driver, you might not get as much from it.