Yes laurel leaves are poisonous if eaten and the tough leaves do take a while to break down in a compost heap if not chopped up by one method or another. I do see in your posted question that you have two advantages.....one is they fall on a small area of your property so they are probably a very manageable number to handle and second is that I assume that you and your neighbor have been living amicably next to each other for a number of years so this situation is not a new one and a solution has been developed by you to adequately process the laurel leaves falling on your property resulting in no harm.

They will rot down at a different rate and the chemicals are toxic to some organisms but the soil ones that normally rot them down are unharmed. So there isn't any problem in mixing them together in your compost bin.

I would go along with Loosestrife's suggestion and if you get a dry spell then collect the leaves by running them over with a hovver mower to chop them up and collect them for the compost.

Thanks all of you for your answers.
The laurel bush/tree isn’t going to be trimmed or cut anytime soon. No agreement on that.
I’ll try and mow over them if they dry out and blend with the grass cuttings. Hopefully one more lawn cut before December. Thanks again

Just to encourage you we have found lawnmowered leaves work very well as a mulch even if they are not rotted. We saw no signs of nitrogen depletion the following year