I have done a three months independent research at a national lab in US with guidance from a scientist who was working there, but he is very busy and not much time is left to ask him to write a recommendation letter (RL) since the application deadline is coming. I want to include this experience in my SOP, and wonder, in general, how is the reaction of graduate admission committees to research experience which is not backed up by a RL?
I believe the research experience with a national lab would be very helpful to your graduate school application. You should do your best to ask that senior scientist to write the recommendation letter for you. And he should understand it's part of his job to write recommendation letters.
In the worst case he will never have time to write the letter, my suggestion is to ask the human resource department of the lab to write a letter to certify that you had worked at that lab. This is, of course, not the recommendation letter. But, at least the certification letter proves that you did work there. How the admission commitee will react is another story. You have no control over it. You just need to do your best!
One of the duties of a researcher who takes on a mentor role is to write letters of recommendation for his students. Your advisor will understand this responsibility. You may want to read the answers to this question regarding writing your own recommendation letter, as this may be relevant to your situation, but you should always be willing to ask for a letter.
You need a letter from the senior person under whom you did the work! If you don't have one, this is like getting a bad letter. People know that they have this responsibility to junior people, so, although, yes, it involves some work on their part, it would be irresponsible to shirk it. You need that letter, I think, or people will wonder...