I use a baby blanket for lap time. I'm not exactley sure what the material is called, it is made of - teddy fleece? I'll attach 2 pictures so you can see, what I mean.
It is really soft and cuddly and my piggies love to snuggle into it. It's also easy to wash, easy to dry and in my experience hair doesn't stick to it like to normal fleece.
I fold it twice, so it's an nice pad, even if an accident happens. My piggies are lap-trained, but when old and/or sick accidents happen.
You can also wrap up a piggy that's afraid. Often they feel more relaxed when in a "piggy buritto". This also prevents too much hair on the clothing.