There are two usages of ~(으)ㄹ까. Also, it's always and only used in questions! You can't make a statement with this grammar point*** 1. ~(으)ㄹ까 indicates that the speaker is pondering/wondering about the conveyed message. By putting the speaker's pondering into a question, ~(으)ㄹ까요 is used in asking the other person's opinion. It goes like this " Do you think . ..?" Ex: "오늘도 효진 씨 수업에 늦게 올까요?" - "Do you think HyoJin will come late to class today?" 2. You can use it to ask someone's opinion or make a polite suggestion. "Shall I/we...?" Ex: 이번 김요일에 같지 점심을 먹을까요?" - Would you like to eat lunch together this Friday? (으)ㄹ래요 also has two usage, but it can be used as a statement or question, depending on how you are using it. 1. When used with in the first person tense, it is used to expresses the intention or will of the speaker. It's almost similar to ~고 싶어요, but (으)ㄹ래요 is slightly more respectful and used in more formal instances. "I'd like to..." Ex: "저는 김밥을 먹을래요"- "I'd like to eat kimbab." 2.When used with another subject, it asks for the thoughts and intentions of the listener. This can be a polite way of asking someone if they want to or can do something either with you or for you. " Ex: "뭘 먹을래요?" - "What would you like to eat?" I hope this was helpful!!!

지금 식사 하실래요? 준비 할까요? Do you want to have your meal now? Shall I prepare it? ~ㄹ래요 is asking about the desire/intention while ~ㄹ까요 isn't.