You have a small lathe and cutting a 3/8 BSW thread in one pass would probably at or more than its limit.
As already said, open up the die, and take more than one pass.
Use a proper lubricant, such Trefolex , Rocol RTD, or if none is available, bacon fat will probably suffice.
use a SLIDING Tailstock Die holder. That relieves the machine or you of dragging the Tailstock along.
The load can easily strip a fine thread as you cut it!
Yes, make up a mandrel Handle, so that you can turn the lathe by hand. It has the advantage that you can feel how much torque is needed. You will break fewer taps that way!
Turning the chuck on a small lathe, to cut a 3/8 coarse thread will require a lot of torque. Probably more than you can apply with a hand gripping the small chuck.
Do check the die, I have had one where the lead in chamfer was not on the marked side, which made life difficult until the error was spotted!
If you do become brave enough to Tap or Die under power, (Be very careful if working upto a shoulder ) use back gear, to reduce the load on the motor.
My lathe is a Craftsman lookalike (6 " swing over the bed ) and with a 1.5 hp motor, I do thread cut under power, using a sliding Die or Tap holder, and plenty of lubricant, at low speed.. If in doubt, the Mandrel Handle is pressed into use.
Being a coward, wherever possible, I avoid screwcutting and use Taps and Dies
But it has just cut a 8 mm pitch half round thread 1.5 mm deep, in several passes using back gear, under power.
You will become more expert as you become more familiar with the machine, and its limitations. Rome was not built in a day!
Howard