This is very common to see palms with yellowing lower leaves. This is due to a lack of certain key nutrients. The best course of action is to fertilize the lawn not with "typical" lawn fertilizer but with a high-quality palm fertilize that has an analysis of 8-2-12 plus 4% Manganese all in a slow-release form.  This is not typically found at the big box store, but rather a very good garden center or horticultural supply store.

So why fertilize the lawn with this fertilizer?  Because to root system of your palms are mixed in with the lawn.  The high nitrogen of most lawn fertilizer upsets the balance of those key nutrients in the palm. 

Even with this fertilizer do not expect to see those leaves turn green.  Also don't remove those yellowing leaves, this only serves to make the problem worse. 

Here is some information on fertilizing palms

http://manatee.ifas.ufl.edu/lawn_and_garden/master-gardener/gardening-manatee-style/p/palm-nutrition...