Hello mili,
Well at 3 your are going to have to be lucky to get your child subitizing. It's probably getting a bit late. But it is possible so keep going.
I started my son on LM at age 4. I wasn't expecting miracles but I did get to see some strong benefits. He did not learn to subitize. What he did learn was number quantity confidence. He was quite sure of how much bigger 20 is compared to 2. This made it so much easier to teach him other math. 6 months later we have given up on LM but he is comfortably doing his sisters grade 1 math work.
So how to get the most of it as an older child? Definately use Icons! Lots of them and many many different ones. 3/4 year olds need to know that 5 of anything is the same as 5 of anything else, quantity speaking. Use icons he will LOVE to look at. Trucks trains and motorbikes and wheels! Insects, superstars, dinosaurs, food...download plenty of variety to keep him interested.
Use the numerals also. At age 3 it's a good time to teach them that a group this big is 12 and this is how we write a 12. Use the numerals after you have showed plenty of quantity cards.
Don't test. Accept that it is unlikely that your child will learn to subitize and don't ask them to give you the answers. If your child does learn to subitize it will be because he is very relaxed and happy during his lessons. Testing doesn't encourage this environment. Show as much as you can of LM before your child gets bored with it. You may last 3 months or maybe 6 or 12 if you are really lucky. Just remember IMPUT IMPUT IMPUT, but continuing with no visible results you are certainly not doing any harm, but are building a good level of math confidence.
Finally don't use LMath as your only math curriculum. Invest in something like Marshmellow math for a good all round grounding. We are using rightstart math with my son. I think it is wonderful! There are a number of (long) informative math threads on this forum. I shall post some links for you for further reading.
http://forum.brillkids.com/teaching-your-child-math/what-are-you-doing-with-your-2-year-olds-for-math/http://forum.brillkids.com/teaching-your-child-math/pick-just-1-program-to-teach-toddler-math/As to grid or random, many say grid for older kids but I used a random assortment.