Blocking L is mainly important because it keeps Kana's submission stat from rising, which leads to the NTR ending if it gets too high. The stat that affects the events that cause Kana to get closer to the MC is the affection stat, which rises steadily as you have dinner with her, block L, take her on dates, yada yada. Some of the affection events specifically trigger after/during dates.
However, also important are the hide-and-seek games, as well as visiting the mansion when L is out of town and finding the secret room. It's these combined things that lead to Kana and MC talking about things, which reveals the big reason behind what L has on Kana and why she's been so afraid. (It's a way better reason than 90% of the NTR H-games out there...) That said, this also puts you on the True Ending path and may stop L's attempts to dick Kana entirely if you trigger the bit where MC confronts him.