The Gillette New deluxe was the range that started around 1929 after the 'Old type' and 'New improved ranges' The range was made for around 16 years and the major upgrade was a slot in the cap and ridge in the guard that prevents any misalignment when inserting or changing a blade.
These razors are not plentiful and I can only assume this was on account of the great depression when wealth and spending was in short supply, add to the fact that Gillette sold millions of the 'Old Type' in the previous two decades and the low numbers that were produced and sold makes even more sense.
It is a good looking razor, but I find the coating on the ones we have found to be of poor quality, and very few are found in good or pristine condition, those are quite expensive also. They were mostly found in the 'Red and Black sets' and 'Bostonian' presentations.
The shave and efficiency is classed as medium by most users, so it is a pretty easy-going razor that will also be good for folks with sensitive skin, probably more so than most earlier models.
Here is a review with some valuable insights to the 'New LC' and 'New Deluxe'
The razor is in good condition with no damage apart from expected wear and tear. This one seems to have been recoated, not the best job, but it is well protected, uniform in colour with no plate loss on any of the parts.