I cut down an old spirea a few summers ago (right to the ground, it was old and never had been pruned) and it came back great! I actually split it up at the same time, and now have a few plants from the one I cut down.
Spireas are really hardy, it should come back good as new.

Spireas just randomly dieback. They're annoying that way. I think they do this even in warmer zones.

Usual case for peony problems is botrytis, especially at this time of year.

What do you mean when you say that older parts of the lilac didn't leaf out? Are there buds that didn't open?

A lot of people I talk to are having issues with trees not leafing out after they bloom, I have that with the new maple in the yard. I thought I was drowning it but the more people I talk to the more common the issue seems to be, maybe the weather? My peonies are just starting to come in the front so maybe the lack of rain is inhibiting them. I have not grown peonies so I am not sure, these were in the yard when I bought the house. I have seen the buds for a month but the leaves are just starting to come

If the soil has built up around the peonies you might remove some or pull it back a bit. I've done that this spring as the mulch has become soil and it dawned on me that I might not get any blooms if roots were buried too much.

About the lilac - I think I'd trim back or even remove the older branches. You can cut out older branches every third year so it shouldn't hurt the bush. My poor lilacs never bloom as the deer have been trimming them too much. This year they are all getting cages.

If your Spirea has growth around the bottom then yes, it will come back good as new. Mine are very slow to leaf this year and some look downright terrible but this cold weather isn't helping matters at all. I was all set to dig one up yesterday and toss it out, thinking it was completely dead, but just as I was about to put the shovel in the ground, I saw buds at the bottom.

Have any other trees or shrubs grown up around your peonies - are they still getting full sun, not crowded by other plants, etc. Tree/shrub roots invading their space can cause a slow decline.

I have a similar situation with my bushes right now. Most everything seems to be leafing out very slowly. Even my trees are acting odd--a swamp oak tree finally has leaves but many branches are leafless or with small leaflets. You might not want to give up on your lilac just yet.

As for your peonies, I would inspect them closely as the season progresses. If its botrytis, here is some advice from A&D peonies:
Botrytis

Botrytis is an airborne fungus that can affect peonies growing any where and can especially be a problem in prolonged wet, cool weather, such as we might have here in the Pacific Northwest. Botrytis can virtually be prevented if you effect a spray program before any botrytis damage is done. Younger peony plants and overfed plants are often most vulnerable. Botrytis can also be minimized and controlled even if your plants get a touch of it.

Signs of blight are stems that rot off at the base or dense gray mold on stems or leaves, blackened buds or blooms or totally limp stems. Immediately clean your plant that is, cut off all affected parts. If using your all purpose garden clippers, wipe with alcohol after peony use.

If only the tip of a leaf is affected, however, only remove the tip, not the whole leaf. Leave as much leaf as you can. Removing infected parts might be all you need to do if you have just a few peonies. Otherwise, a spray program may be necessary. For best results start your spray program when stems are up 5 or 6 inches then continue spraying once every week to 10 days until bloom time. Spray the plant, drip spray down the stem into the ground and spray the ground around the plant.

Fungicides approved for peonies include captan, copper sulphate (try Lilly Miller Micro-Cop), Daconil (chlorothalonil), Mancozeb, Maneb, Bravo or professional fungicides such as Decree, Chipco 26019 or ClearyÂs 3336 (thiophanate methyl). A new systemic fungicide is TM85 and another is offered by Cleary's. Follow label directions carefully. Mixing up such sprays carelessly and adding too much surfactant can sometimes cause more damage than the botyritis.

Occurrences of botrytis are a natural part of growing peonies, but we've never had to destroy a peony because of it. It rarely harms the root itself, unless left untreated for years.

thanks for all of your help everyone. Yesterday after watching a web video on transplanting peonies I dug up the Sorbet thinking perhaps it just needed a dividing....there was a large tangle of roots and very few eyes to be found. I feel like I really butchered the poor thing but planted the few salvageable parts anyway. I've never divided a peony before - what are the chances it will come back???? that's good news about the spirea as I wasn't relishing the idea of digging it out too. yes, it seems like an odd growing season everywhere here in western canada....cold, dry,...snow...hail....has anyone read the Farmer's Almanac forecast for the prairies?

Peonies never need to be divided. They hate being moved.

PS: I didn't find any signs of botrytus thankfully and yes, the leaf buds on the older part of the lilac were coming along normally 3 weeks ago and then just came to a standstill. The newer branches have leafed out fine and there are blossoms coming on those.... The older portion of the shrub isn't dead as a doornail yet - it just has no leaves!!!!! Its just whether to cut back now or hope for some late development????