I would not be overly concerned about 93L unless it redevelops convection closer to the center of circulation. The old convection seems to be slowly fading as it moves away to the east.

They have scheduled recon flights into 93L for tomorrow, making for a busy recon POD:

I. ATLANTIC REQUIREMENTS

1. SUSPECT AREA (GULF OF MEXICO)
FLIGHT ONE FLIGHT TWO
A. 06/1500Z A. 07/0300,0900Z
B. AFXXX 01IIA INVEST B. NOAA2 02IIA CYCLONE
C. 06/1230Z C. 07/0130Z
D. 25.0N 84.0W D. 26.0N 83.0W
E. 06/1400Z TO 06/1930Z E. 07/0200Z TO 07/0930Z
F. SFC TO 10,000 FT F. SFC TO 10,000 FT

FLIGHT THREE
A. 07/1200,1500,1800Z E. 07/1030Z TO 07/1830Z
B. AFXXX 03IIA CYCLONE F. SFC TO 10,000 FT
C. 07/0900Z
D. 27.0N 82.5W

2. TROPICAL STORM TAMMY
FLIGHT ONE
A. 06/1500,2100Z
B. AFXXX 0321A TAMMY
C. 06/1245Z
D. 31.0N 81.0W
E. 06/1330Z TO 06/2130Z
F. SFC TO 10,000 FT

2. SUCCEEDING DAY OUTLOOK: CONTINUE 3-HOURLY FIXES ON SUSPECT
AREA IF IT DEVELOPS AND IS A THREAT.