I know it is TA's responsibility to help students understand the course material. But there are always some students don't like to think independently, or maybe just not smart enough. Is it ok for TA to tell students that "I can't help you. You should figure it out by youself." for some lame questions? Would this put TA into dereliction of duty?
My job as an instructor is to help the students learn, and I try to do so to the best of my abilities.
- If a student is asking very basic questions (don't call them lame ever), help them to get up to speed pointing at some reading. You should pay attention to this, since for every student that asks questions, there may be several silent ones, and it may be an indication that the cohort is missing some knowledge your course is assuming.
- If they ask questions for which they know the answer, but are unsure, teach them how to validate and verify their answers.
- If they ask every little step of the way, the Socratic method is an option: ask questions back, make them work for the answers. But make them helpful: use them to guide the student towards the answer.
- The students that just ask very many questions, just get lower priority, since I have to take care of the whole group, but I do still help them.
- Questions that are off topic can be either gently shot down and redirected, or quickly point them at some references. If you find the question particularly interesting, you can offer to give more details after class. Make sure they don't get lost in the sidetracks, though.
In general, the goal should be to try to make yourself redundant by teaching them how to not need you you. This is never going to actually happen, but it is a worthy sky to look up to.
As an instructor, you should bear in mind that your goal is to teach, not to supply answers - sometimes that does mean getting a student to work something out on their own. But there are two major things to keep in mind: even in your own head, it's not good to think of questions as "lame" unless you think they aren't being asked in good faith - by which I mean, the only "lame" or "bad" questions are questions that are intentionally asked to annoy you. If the student is genuinely having trouble, it is certainly the responsibility of the TA or instructor to help (within the time they're being paid for, at least).
That doesn't mean you have to give the answer. As Davidmh pointed out in their answer, the Socratic method can be a great way to go; respond to their question with a question of your own, forcing the student to think about it. If you feel like your students are often asking questions they "ought" to be able to figure out on their own, then if I were you I'd change my focus; concentrate more on teaching them how to figure things out, rather than just on the material. For example, I teach math; one technique I'm fond of is generalization: when a student comes to me with a problem I think they can solve on their own, I'll just repeat broad generalizations to them (e.g., "a good way to start any math problem is by naming things. What looks like it wants a name in this problem?") until they get the ball rolling on their own. I'm not giving them any new information, or even any information specific to the problem, just sort of prodding them in a good general direction.
Also: I don't know what field you're in, but in math confidence is a major issue. Many students will ask endless questions because they're afraid of getting a problem wrong. I try to counteract that by teaching them (a) how to recognize that they've gone in the wrong direction, and (b) that going in the wrong direction isn't bad as long as you can fix it. Once they get used to that idea, they get more comfortable with making mistakes and don't need me to help them along as much.
One line answer: yes, but your answer should provoke their interest and make them think deeper, make them wonder about the problem.
No. You should refer the student to the professor if s/he doesn't feel satisfied with your explanation. On the other hand, if you don't feel satisfied with your explanation, then please delve deeper into the material on your own time; you may seek help from fellow grad students and/or from professors.
Don't hesitate to tell the student you don't have a good answer off the top of your head, but you will look into it.