LfT would certainly be suitable for home. On the Special Needs section there are at least 7 or 8 of us using it right now 
You start by doing a short (5 minute) assessment - there is a picture accompanied by 4 or 5 short sentences. You ask the questions and note the exact answer your DS gives. The questions range from 'Where is Philip?' 'What is Philip doing?, etc., to much more abstract questions 'Philip doesn't have any money for popcorn, what could he do?', etc. For each question you give a score (0-3) depending on how relevant and accurate the answer was. That score indicates a 'starting point' for the scenarios.
The idea is that you are starting at a level your child will cope with, so that you and they see progress.
Then, you use a scenario. Again, no more than 5 minutes. Afterwards you go over the scenario with the child, discussing the questions and modeling 'good' answers as you go. You make sure you have recorded everything they said. You also record their score.
The next day you do the same scenario. The hope is that by going over it the day before, you have helped your child to develop their understanding. You follow the same procedure.
The third day you do the same scenario one last time. Again, you discuss afterwards and model good answers.
It's important to do it no more than 3 times, because you risk the child rote learning the answers, rather than building their language.
Obviously, if your child does perfectly well at the scenario, you don't need to repeat it.
So, you may find that your child scores 11/18 on day 1, 12/18 on day 2 and 15/18 on day 3.
On the 4th day, you do the next scenario, which you may repeat on day 5, and 6.
There are 3 'modules' - picture and text read by you, picture and text read by your DS, then just text. There are also 3 'language levels' A, B and C, which denote the complexity of the questions. Most people find that as they move up a module, they have to move down a language level at first.