Yes, it is quite possible, but not cheap. They are a lot smaller than full sized quilts and take a lot less time. If you do have friends tie them, they will be faster, as well.
But, I also wonder about giving lap quilts to the homeless. Are these homeless men or women? Do they live in a shelter? Do they even want them?
I ask all these things, because I give away a lot of quilts here in Poland. I am not sure that the homeless here would actually utilize a quilt. A blanket would be a bit easier to carry around. And, frankly, if it is for the homeless who aren't looking to change, as opposed to a person who is going through a hard time, then maybe making those "ugly quilts" as some groups do, would be entirely appropriate. (I know that some believe that only beautiful quilts should be given to charity, and this isn't meant as a criticism, just an observation.)
I think it just means knowing your target group. If it is women who are homeless, but will soon be in a home again, then by all means, go for it, but if they are men who are homeless because they prefer the streets or tents to a shelter or home, then you need to decide if you are wasting your money on something beautiful for them. They would do fine with two sheets tied with a blanket in the middle for warmth since beauty means nothing to them. Save your money and effort for someone who will actually appreciate it and maybe even cry over how beautiful it is and how much it means to them.
But, yes, it is possible. Money is needed, however. If the girls' sewing skills are limited, she will need help.