Yes.
There were 4 versions of the LT77. It was used on many vehicles, LRs, Rovers, TVRs, Morgans..etc. The later version (mid-80s on) is the best of the lot. They are a "notchy" shift and not rated for much bhp.
They have an internal lubrication pump which is very sensitive to which transmission fluid is used. Use the wrong one and the results can be sad in as little as a few miles. Despite this, the wrong fluid is OFTEN used. A LT77 takes ATF (yes ATF!) Dextron 2 or 3.
The R380 is a far more modern box. Outside of its ratios and length (3hich makes it a LT77 swap), it shares nothing with the LT77s. It is rated for almost double the bhp as the LT77s and has a very liquidy shift.
However. it too needs the right fluid. A MTF94. That is Castrol SMX-S. (If you are in North America, it is not sold. In that area of the world, go for Amsoil Synthetic Manual Synchromesh Transmission Fluid (MTF) SAE 5W-30
The R380 comes in many configurations for different vehicles..unlike the LT77. Try to get one made after March 1999.
Both the LT77 and the R380 should never be towed with the rear wheels on the ground.