Risky? (LXLightXReader)

I have been working with L on the Kira case for about a month now. L suspects Light Yagami as Kira. Me? I'm not sure...It sounds reasonable enough. "(Y/N)? (Y/N) wake up." Light shook me and I woke up to see I fell asleep at the desk. The lights from the computer blinded as I sat up. Once my eyes adjusted I looked up and saw that L was looking at me. 

"S-Sorry," I stuttered and felt my cheeks heat up from the embarrassment of the situation. 

"It's fine. You have been working late with the Kira case," L said.  "You should go home and rest," L added. 

"You sure?" I asked.

 "Yes." L replied and I got up, stretching my arms to try to loosen the muscles that had tightened due to my sleeping position. 

"See you tomorrow." I waved as I walked out of the building. 

I yawned. It feels like we're not getting anywhere with this case. My apartment soon comes into view and I dig around my pocket for the keys. When I unlock the door I immediately head towards the couch and plop down on it. I can't believe I fell asleep at work. Luckily, L was pretty understanding. Still, I shouldn't make this a habit. There is a very important case to solve after all. 

My stomach growled, breaking the silence and my thought process. I got up and went into the kitchen to make myself something to eat. After finishing my small meal, I walked to my room, plopped down on the bed and fell asleep the minute my eyes were closed. I woke up to the warm sunlight shining on my face through my curtains. Glancing  at the clock my stomach drops as I realize it's 12:00pm. Is it really that late? I quickly got out of bed and did my normal morning routine. 

Once my morning ritual was all said and done with, I quickly headed to the station. I walked in the room where L was and sat next to him. "Sorry I'm late," I apologized. 

"It's fine. Come in whenever you want," L said. I gave a short nod. 

"Good afternoon, (Y/N)" I heard a familiar voice say. I looked back to see Light smiling at me. 

"Afternoon," I greeted and gave a small wave. L's eyes were glued to the screen. I saw that he had a plate with cake on it and a strawberry resting on top of the icing. My stomach growled and L looked over at me. 

"Have you not eaten yet?" he asked.

 "No..." I said sheepishly. 

"I'll take her to lunch," Light said. I blushed. Going out to lunch with Light? "If...It's okay with Ryuzaki," Light added and I looked over to L.

 He sighed and hesitantly said "Alright." I got up and left the station with Light. We walked on the sidewalk weaving our way past crowds. 

"Thank you," I said. 

"It's no problem," he said and I smiled. I wanted to hug him, but I didn't want it to be too awkward. 

"Here we are. This café has pretty good food," he said and held the door open for me. I walked in and went to the counter and looked at the menu. 

"How can I help you?" the guy said. 

"I would like a club sandwich with hot oolong, please," I ordered. 

"Okay, anything else?" he asked. 

"No that's it," Light said and paid for it. We walked to a table and sat. I wanted to discuss the Kira case with him, but I couldn't. Not with all these people around. A guy brought my food and walked off. I took a bite of my sandwich. It was so good! Light wasn't kidding when he said this place had good food. I took a sip of my tea and yelped a little. 

"What's wrong?" Light asked. I put my tea down. 

"I burned my tongue," I replied. 

"Are you okay?" he asked. 

"Yeah, I'm fine." I said and took another bite of my sandwich. When I glanced up I saw Light was glaring at something. 

"What's wrong?" I asked. 

"That guy that took your order keeps staring at you," he said and I looked over to see him quickly look away. I smiled a little and finished my sandwich. We got up and left when I was through with my lunch. Was he jealous? I wondered. I looked around to make sure no one was around. 

"So, Ryuzaki accuses you of being Kira," I said, deciding to swallow my anxiety. I wanted to see what he had to say. Maybe I wanted him to convince me that he wasn't. 

"Do you believe I am?" he asked. 

"I'm not sure..." I answered. Light was silent for a little bit.

 "What if I was?" he asked. My stomach dropped and my heart rate began to increase.

"I...don't know. You aren't saying that you are, are you?" I asked, trying to remain calm.

"No, I was just curious," he said and we arrived at the station.