I never had a problem with either before this year. It has been so hot and humid and some of my plants are suffering with rust and mildew. Will it kill the plants or will they return alright next year? Thanks for your help.

Plants get both Rust and the Mildews every year and mostly survive just fine. Hollyhocks are often peppered with the Rust nodules and keep on growing, although they struggle, and blossom and produce seed that grows the following year.
Lilacs, and many other plants, get Powdery Mildew which does not appear to affect them much at all. Downy Mildew may well be different.
Neither of these are very attractive which is why most people take steps to try and control them.

owie, it will depend on how bad it gets. The rust killed my hollyhocks this year. It was the worst I've ever seen. Many other years they have managed to still grow & bloom. So I'll plant them in a different place for blooms next year.
You might call your county extension office & see what they have to say since they will know the conditions in your area better than those of us on these boards.

Thanks. ga karen, I not going to do anything with them anyway so I won't call the extension office. I was just wondering waht I should expect. I think they are speedwells. They have been in the ground for several years.

Probably it would but just keep a look at them , maybe they'll survive.

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You shouldn't just pass off rust and mildew as just something that is common; they are dangerous to the plants.
Rust is caused by a fungus and may be a type that that particular plant is susceptible to.
A fungicide, sprayed, or dusted often, early in the plant development, can slow down or eliminate somewhat, the effects of rust on hollyhocks.
The thing to do though, is to keep the undersides of the plants as clean as possible so that the fungus spores cant invade the soil where it stays--sometimes for as long as two years.
Its always a good idea to keep the area under plants and trees clean so that disease can be kept to a minimum.
Powdery Mildew, also a fungus, can be treated with different materials such as fungicide, lime/copper sulfate (Bordeaux Mixture) petroleum oils, baking soda, and many other concoctions.
Also, letting the plants be subject to air currents, slows down and may stop mildew.

Interesting this yr. I've always had meldew on my bee balm. I pulled everything away from it this yr. Giving it space and air and no meldew. I'm really amazed. But it isn't as big as it was last yr. What's up with that??