We did lap napping exclusively during the day for the first 4 months - then I got rid of DS's dummy and he no longer wanted my lap! I couldn't believe the freedom I had when I got him to nap in his cot.
I think you have to be persistent. Just go cold turkey and ban naps on your lap. He's old enough now. Just put him down in his cot at nap time and give him a little comforting, just whatever you do at night time.
Congrats on expecting No2, that mean's it's definitely time to end it!!
My mother fixed this problem with my DD (4 months). We now put her in her buggy, put a blanket or muslin over between the hood and bumper bar and rock vigorously for 5 or 10 min. She then naps in her buggy. If she wakes then she can be rocked again. I was amazed at how quickly she took to this. She also will sit in her buggy and watch one of us do things.
I forgot to say that we do wait until she looks sleepy to do this (eye rubbing and yawning) and she sometimes does cry a little before falling asleep, but she knows that someone is there as she is being rocked and it is a falling asleep cry rather than a frantic cry. Also I often give her something to hold, like a soft book or soft toy.