Fanfiction.net is also a good place. It has a huge collection of 'Supernatural' fanfictions. However, the search function might not be as refined as AO3. But if you patiently browse through the 'Supernatural' section and look for tags related to Lucifer and hurt/comfort, you're likely to find some great reads.
You can start by looking on popular fanfiction websites like Archive of Our Own (AO3). There are a large number of 'Supernatural' fanfictions there, and you can use the search filters to specifically look for Lucifer - related hurt/comfort ones. Just type in 'Supernatural' and 'Lucifer' along with 'hurt/comfort' in the search bar.
Another option is Tumblr. There are many fanfiction communities on Tumblr. You can search for relevant blogs or posts using the keywords 'Supernatural', 'Lucifer', 'hurt comfort'. Some bloggers might also recommend their favorite fanfictions, which can be a great way to discover some hidden gems.
Chapter 519, "I'm Here to Participate in the Program", is the clearest early answer because it turns Younger President Jin's situation into a concrete plot event.
Chapter 287, "Saved", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. It opens with For five consecutive days, the search and rescue team had not... and closes on Failing to obtain any news after numerous attempts, Lu Xingchao had....
Chapter 408, "You Can't Be on the Same Team!", is the clearest early answer because it turns Flash Change's situation into a concrete plot event. The chapter gives readers a real answer by opening on Zheng Xun fell silent after he understood the situation.
Chapter 265, "This Time You Must Help Me", is the clearest early answer because it turns Weibo's situation into a concrete plot event.
Chapter 581, "Where is everyone? Where have they all gone?!", is the clearest early answer because it turns Are's situation into a concrete plot event.
Chapter 376, "I'm Just Afraid You Don't Need Me Anymore", is the clearest early answer because it turns Crown Prince Jin's situation into a concrete plot event. The chapter gives readers a real answer by opening on The phone call fell into a long silence.
Chapter 300, "You're retaking the college entrance exam?!", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. A useful checkpoint is the way the scene starts with I dropped out." Jiang Li said calmly.
Chapter 513, "A Public Stage", is the clearest early answer because it turns Jiang Shixu's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Everyone was sharing their experiences in a few words, the banter...
Chapter 786, "Working at Chen'an?!", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. It opens with When Jiang Li left Taiqi's office building, it was already getting... and closes on She recognized that this must be the streamer Xiao Xue..
Chapter 761, "Can You Take Us In?", is the clearest early answer because it turns Aunt Feng's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Lili, this is your maternal uncle's family..." Jiang Li lifted her...