How far are you in the LOF elementary series? We're in E now, and I find it to cover lots and be well-designed. It SEEMS random, but when you keep plugging away, you see the repetition and the building of concepts. It's fine to use other things too, but LOF is better than I think you think it is. :)
We're only up to 2nd grade right now, so it may be that with a 4th grader you'd need to go farther in the LOF books to really get what you are looking for.
I think you may be correct. We started LOF in September and haven't been doing it daily. My daughter is in book 'E' and my son is in book 'D'. My daughter works in spurts and will do quite a few chapters but not often. My son likes to do one or two chapters a few times/week. (I was comfortable using LOF alone until my son expressed an interest in going to PS for 5th grade and he said he does not want to be behind. My concern was magnified because when I was on the board of the charter school they attended in 1st grade, I heard many times how important it was for the school to be two grade levels ahead in math. I wasn't sure if the regular public school had the same attitude.) Even if we purchase Singapore Math, I want to continue with LOF because my children and I like the series. And, we already have the Elementary, Intermediate, and Fraction books. The teacher my children see 1x/week gave them the Key to Fractions book last week and she said they finished 1/2 of it in one sitting on their own and didn't want to stop when it was time to leave. (She is an ex Montessori teacher but runs her homeschool classes using a Sudbury model.) I've asked her to make sure she covers some math and she intends to give them the Key to Decimals book next. So, I think we are attacking math from several directions. Well see what we end up using. (Actually math is the only subject we are 'attacking'. I am not sure if I am unschooling the other subjects or just being an incompetent homeschooler! I love the idea of unschooling but am too worried about math to trust the process.)
I haven't ordered Singapore Math yet. Someone else suggested RightStart and I started doing more research; but stopped because I was driving myself crazy! So...the kids took the Singapore placement tests today. Their immediate reaction was crying that they didn't know how to do any of it. They thought it was a test and coming from Montessori with no tests, they panicked. But once they calmed down they did better. They had trouble understanding what was wanted. e.g. If the paper said "What is the difference between 1100 and 763?" They said they didn't understand 'difference' between two numbers. But when I told them what was wanted they could do the work. This happened repeatedly, so I know they need practice doing math in a more traditional manner. I am considering ordering the 3B workbooks and let them work through the workbooks. I will also order the textbook so we can use it for weak areas but we will not necessarily go through the entire 3B text book.
I hope this makes sense...I have a migraine today - ugh!