I still have no clue how some don't understand how the time travelling in Lovely Runner goes when there was explanations thrown all over the show that excludes too much exposition because, let's face it, it's a romantic drama.
SPOILER WARNING.
1. The watch was believed to be tampered with by Im Malja. She held the watch the same day Sol met Sunjae, kept the watch safe on Sol's third trip to the past, and was the person who threw the watch away because only her— with Sol and Sunjae— know the power it had.
2. The watch only activates the moment Sunjae dies. He dies at 12am in January of 2023 + May 7th 2009, so Sol is free to use it after it activates. However, it also shows some sign of pre-activation to the user as a warning— which is why Sol saw it lightning up on episode 1 and episode 13.
3. She's not allowed to use it within the 24 hours of it's usage, and the longer she stays in the future, the longer time would pass on the past. That's why on her second time travel, there was a 10 days gap— but due to her having to have lost the watch for long period of time in episode 9, months have passed instead. (This is almost like a reference to Narnia.)
4. She's unable to say anything about the future as time stops when she does. However, if it's the other person talking to her and asking questions, she's allowed to answer. That's why Sunjae was able to understand her time travelling mechanics without the time stopping for her. It's him supplying himself with information, not her.
5. “The brain may have forgotten the memories, but they seep into your soul.” This was Malja's hint to Sol. Sunjae's connection to the watch led him to remember every timeline he had with Sol. He had several triggers in the drama and was the most affected by the changes she made. It's also not like Sunjae was the only one affected by this. Taesung, Inhyuk, Sunjae's dad and even Taesung's dad felt some time of connection with Sol and felt like they know her. They may have had a hard time making recollections about it, but it's there— written in their DNA. (Also, while this is fantasy, this could be a different form of ‘deja vu’. We all experienced that. It's not a myth.)
/6. I explained this before: why was Sol able to remember bits and pieces of the future— specially the part where Youngsoo will attack her at the cliff and Sunjae would die for it, that's why she had to leave the train as to not implicate him:
This is her last time travel. Her brain is rewiring the new chain of events based on the memory that 2009 Sol was experiencing that 34 Sol was recollecting at that time. Since it's her last chance using that watch, it was supposed to be the FIXED timeline after all the time travels that she had. Hence, the ‘vision of the future’.
There are no parallel timelines in Lovely Runner, just one. Everything that Sol did in the past will just rewrite the future, that includes the time traveler Sol and the past Sol. The reason that Sol of the future can't seem to recollect them (OG timeline, 1st travel and 2nd travel) is because past Sol blocks them out due to trauma. Third timeline Sol never got to experience such trauma that's why 34 Sol had no problem remembering Sunjae's death on episode 13.
Anyway, that's all.
My answer is Lovely Runner, by the way.