The studio may not be in existence, but I think it was the Lindsay Studio of C. L. Lindsay.

In 1930,
C. L. Lindsay (30) is in Meridian Mississippi.
His occupation is Photographer, in a photo shop. His wife was the assistant.
This may have been Clinton Lindsay.

There are a couple of Clinton Lindsays in the records.

A Clinton Lindsay registered for the WWI Draft in Lauderdale County, MS.
He had relatives in nearby Clarke County, MS.
----------
I couldn't find anything definitive on "Phelps".
It may have been a reference to a surname. There were many Phelps families in nearby counties.