I know the Carolinas are not good Andromeda so instead of relocating the plants make certain to mulch heavily and water more often and if that doesn't work then remove them in the fall to a shadier location. As for lace bugs if you are certain that's what they are then read the following:

Tolerate lace bugs when possible. Natural enemies, such as lady beetles, green lacewings, and other predators help keep lace bugs in check. When natural enemies are present, lace bugs generally cause little damage to the plant.

A high-pressure water spray from a garden hose is an option for managing lace bug nymphs on small plants. The water spray acts much like a heavy rain, knocking nymphs off the plant. Since nymphs can not fly back to the plant, they are less likely to survive. Direct the spray at the undersides of the leaves where most lace bugs are found.

Insecticides can be effective in reducing numbers of lace bugs on plants. Use insecticides judiciously, as they kill natural enemies as well as lace bugs, and can make lace bug problems worse. Avoid spraying broad-spectrum insecticides (i.e., acephate, carbaryl, and chlorpyrifos) when possible to preserve natural enemies for good long-term management.

When using insecticides, good coverage is critical. Be sure to spray the undersides of the leaves where lace bugs are normally found.

It is best to use the least toxic products first. Insecticidal soaps (e.g., Safer's), horticultural oils, and pyrethrins are insecticide products with relatively low toxicity, and are relatively safe for many beneficial insects including natural enemies. Other products to manage lace bugs are cyfluthrin, permethrin, carbaryl (e.g., Sevin), or acephate (e.g., Orthene).

Here is a link that might be useful: Propagating Perennials

I inherited a Pieris Japonica in a sunny spot when I moved here. I tolerated and treated the foliage for quite a few years until I finally bit the bullet and moved it to almost full shade (2 hrs morning sun) and dry (competition with pine tree roots).

I pruned it and babied it for a couple of years (water, Hollytone, compost, mulch). Its now trouble free and has filled back in and beautiful. Its a great background for my shady perennial garden. It doesn't bloom all that much but I think that is partly because of our winters. I get plenty of flower buds but usually just blooms below the snow line.

I wouldn't fertilize right away after transplanting. YOu want the roots to settle in before the plant tries to put out new growth. A transplant solution would be fine though. And Lots of watering the first year (preferably 2).

Ironically, I replaced my pieris with a holly! I first tried Dragon Lady, but that was borderline hardy. It struggled during unusually super cold snaps. I then replaced it with Ilex meserve 'Blue Princess' and it is doing fine, but it is a slow grower. I added a new variety (more columnar) next to it at the far end of the house last year, Castlespire. Its doing well too.

As far as deer, I couldn't say for sure, but I would guess yes. I rarely have deer, but on occasion they have gone for the yews in the backyard. They haven't needed to come close to the house (yet!). I put Irish Soap half bars all around as a preventative and I think it works.

{{gwi:243788}}

I thank both of you for your answers.
I think I will transplant them to a morning sun spot that has acidic soil.
I have other Pieris there and they are doing very well.
Now I need something 2-3 feet, that likes sun, flowers and deer don't eat.
Any ideas?

Depending on what zone you live in and if you are within their range Potentilla Kay Dykes would fill the bill 110%.

Here is a link that might be useful: Propagating Perennials

Native P. floribunda probably a better choice for many eastern sites. Wouldn't expect much deer action, like their relatives the rhododendrons these are poisonous. When I saw a presentation on looking for rhododendrons on Yaku Island it was claimed you couldn't drink out of the streams there because the pieris had poisoned them. Speaker showed a picture of pieris lining a stream.

I live in NJ not in NC and not on the shore. I am 20 miles from Easton, PA.
No one commented on when to fertilize and when to treat for lace bugs!

Sample your soil and have it tested to see about fertilizer, buy a product that provides what's lacking (if anything) and is labeled for heath family shrubs like pieris (you don't want an alkaline fertilizer like might be used on lilacs) and apply according to label directions.

I have lacebug problems too and my plants are not in full sun. I would be afraid of moving an infected shrub closer to the non-infected shrubs.
I have been looking into this myself. Andromeda Lace bugs overwinter in the egg stage attached to the leaves. First generation hatches Mid May, second in Mid-late July and third late summer, early fall.
Some options I've found...
Use jets of water to dislodge nymphs after hatching.
Spray nymphs with insecticidal soaps, horticultural oil or neem oil with each hatching, get under leaves, contact the nymphs.
Predators are: assassin bugs, lacewing larvae, lady beetles, jumping spiders, pirate bugs, and predaceous mites but predators show up after damage.
Then there are synthetic pesticides and systemic insecticides which I prefer not to use as my yard has built up a descent population of beneficials over the years. I have several lady beetles and Hoover flies doing a good job on other pests. I might look into some Lacewings. I don't know much about predaceous mites but it seems those crazy red mites that run everywhere might be considered one.
As far as cutting off the old foliage, I see plenty of people trim andromeda back but I have been reluctant to as they grow so slowly and since it has lacebugs, the foliage isn't the healthiest. Maybe someone else can comment on that.