How do I thicken my dessert?
Try taking a very small amount of your lemon soup and see what happens if you do heat it to a simmer. It might work, but if it doesn't you won't have ruined the whole thing.

If not successful, then you might need to reimagine the dessert. My first thought would be to fill and/or saturate some dessert shells or angel food cake with the mixture, and then firm it up by chilling or freezing it.