Last Date, the side-quest available in Yusnaan, the second city featured in Lightning Returns: FF 13 is a short quest, yet it can be failed, if you don’t complete it within the allotted time.
Last Date becomes available after you complete the third main-quest in Yusnaan, named A Solitary Patron, and after 11 AM, when Lennet, the quest giver, spawns within the city.
Furthermore, the side-quest requires a specific item, and the following walkthrough includes useful information on how to complete Last Date in Lightning Returns: Final Fantasy XIII.
Description: “Lightning runs into a crestfallen young man by the name of Lennet who makes a surprising suggestion – he asks Lightning for a date, in place of the girl who canceled on him. If Lightning feels sorry enough for the young man, she should don her best outfit, and meet him at the Banquet of the Lord, in the Glutton’s Quarter. Lightning must complete the quest within the next three days. The date must take place between seven and eleven o’clock in the evening.”
Requirements: Start at 11 AM, after Main Quest 2-3: A Solitary Patron.
Continue the quest after 7PM, same day.
Rewards: 500 Gil, Maximum HP + 50, Strength + 3, Magic + 5, Crystal Heart Adornment
The first step for this specific quest is to make sure that the clock shows 11 AM, and that you finish A Solitary Patron main-quest by defeating Snow. Now, you will have to open your map and head north, towards the Yusnaan Train Station.
From there head east in the Glutton’s Quarter until you reach the stairs that lead to The Banquet of the Lord restaurant.
If you have completed Family Food side-quest, it is the same restaurant where you have found Gordon Gourmet.
At the bottom of the stairs you should see a NPC wearing a white jacket. Talk to him and he will tell you that he had a date with his girlfriend, but she dumped him. Accept the quest and you will be asked to date Lennet, but the date starts at 7 PM.
Note: At this point you should focus on other side-quests and return to the restaurant at 7 PM, but make sure that you don’t let the day pass. Try to date Lennet the same day, or you may fail the quest.
When you get to the Banquet of The Lord, at 7 PM, open your inventory and equip the Midnight Mauve garb acquired from Zoe (The Fighting Actress side-quest).
While wearing the beautiful dress talk to Lennet who sits at the table in The Banquet of The Lord, and watch the fireworks with him. After the cutscene, the Last Date side quest ends.