Minimum Equipment List, MEL, is just that: the MINIMUM EQUIPMENT LIST.
It lists those variations which can be accommodated in case of failed items or parts of them, anything not listed is a NO-GO, unless it can be placed under a generic heading.
In case of B737 MEL 33-14 Exterior Emergency Lighting System, it reads:
a) May be inoperative for day operations.
b) A single exit light may be inoperative for night operations, provided the provisions of MEL 52-16 are applied to the affected exit.
The referred to item 52-16. Emergency Exits (including Passenger Entry Doors, Galley Service Doors and Overwing Exits excluding flight Deck Emergency Exits) reads in turn:
(M) (O) One Exit may be inoperative provided
a) It is not reasonably practicable to repair the inoperative exit before the commencment of the fight.
b) Not more than 72 hours have elapsed since the exit became inoperative.
c) The aircraft does not exceed five (5) further flights with the exit inoperative.
d) The procedures detailed in DDPG 52-16 are followed.
DDPG 52-16 refers to "The exit unservicable placard must be affixed to the inoperative exit prior to passenger embarkation.", thus
MAINTENANCE (M)
1. The exit must be latched closed and not used for any purpose, and all associated exit / and or emergency exit markings , signs, and lights must be obscured.
2. The strip floor lighting at the exit must be masked.
3. All other exits and escape slides must be fully operative.
4. Tapes or ropes of conspicuous colours shall be installed to block access to unusable seats prior to bording of passengers.
OPERATIONS (O)
1. Persons (other than assigned cabin attendants) are not permitted to be seated in the blocked area.
2. The pre-take-off briefing to passengers must accurately represent the current state and condition of the aircraft’s escape facilities. An oral briefing by cabin staff, or a breifing using audio/visual means or a breifing by reference to a briefing card, must be immediately qualified by an oral announcement to draw the attention of passengers to the fact that a particular exit is inoperative and displays a exit unservicable placard.
3. Where the evacuation drill calls for cabin crew to be seated by the inoperative exit, they are breifed to direct passengers to a servicable exit.
4. Passenger reductions and seating configurations shall not deviate from those detailed in Figures 52-16 (a) to (d) on the following pages. These seating diagrams shall cover the following circumstances:
- Aft Door or Slide inoperative (LH or RH). [63/189 pax maximum]
- Forward Door or Slide inoperative (LH or RH). [63/189 pax maximum]
- Fwd Overwing Exit inoperative. [144/189 pax maximum]
- Aft Overwing Exit inoperative. [108/189 pax maximum]
5. The Adjusted Weights Loadsheet remains valid under the conditions of ...
6. The affected emergency exit and blocked seating layout are checked before each flight by the relevant cabin crew member.
7. The escape path to the affected emergency exit is checked by the relevant cabin crew member to be unobstructed before each takeoff and landing.
So in conclusion, you CAN depart at night with ONE exterior Emergency Exit light unserviceable provided the AFFECTED EXIT is NOT used for operational reasons, this may require reducing pax numbers as per YOUR DDPG, the mentioned numbers are for a 189 seat configuration.