List of resistant plants in link. To a certain extent, it may be a cultural problem (excess water, insufficient drainage). Davis states fungicide fosetyl-al (Aliette) may help, but a tree that can stand up to living in a lawn is likely the way to go.

River birch, Ginko, Liquidambar, Magnolia listed as resistant, but Liquidambar has a lot of problems all its own. Some Magnolia can get huge with huge root systems, choose carefully. Ginko (male cultivars only, females had stinky fruit) are quite nice. Also check the Sunset Western Garden Book, I think they have a category of "trees that do well in lawns".

Here is a link that might be useful: phytothoptera resistant plants

Thanks for the info. I forgot to mention I had planted a birch tree next to my alder just a few months back (before I noticed my alder was dying), however I don't think it is a river birch. It may be a silver birch. Is this likely to get the disease as well?

Birch is likely to have a very short life in your lawn. The folks planted three here that were lovely while they lasted. Al