I bought English lavender ‘grosso’ and some sort of variegated thyme I forgot the cultivar

I think the thyme is called hi ho silver

'Grosso' is a hybrid cultivar and somewhat less winter hardy than true English lavender (Lavandula angustifolia),

You should also be aware that often heavily variegated are not always as robust and hardy as their solid colored cousins.

It’s all my garden center sells. I already have both of them, I’ll try to see if they survive if I mulch them

Watch out for a mulch holding too much moisture close to the plant, especially if you receive a heavy snow cover. As stated, sharp, fast drainage is probably more critical to their ability to overwinter than cold.

I have grown them many times (6a) and have never had either survive.

Years and years ago, I had good luck with 'Lady' lavender. I grew a hedge of it from seed, and it even produced some volunteers. Munsted survived a year or two. I planted Phenomenal this spring. Others have reported good luck with it.

Creeping thyme is slowly taking over the parts of my lawn where there is a thin layer of soil over bedrock. DH has been threatening to buy some culinary thyme for a couple of years now, so I haven't.

IME, the necessity for excellent drainage is overstated. I have a heavy, slightly alkaline soil that many people would call clay. I don't think lavender can handle the combination of acidic soil, and averagely draining soil, so you may be OK with the right cultivar.

I wonder what kills it over winter

What if I put it under a covered area outside? Will it survive then?

I have a few cultivars of creeping thyme and several large clumps of ”Phenomenal” lavender that have overwintered for me for at least six years now in a solid zone 5b.

If you have somewhere south facing under an overhang, it is worth trying. The idea is to protect from rain, but have as much sun as possible.

I used to know people who had a certain amount of success growing things like Aril iris under those conditions.

Creeping thyme certainly survives here without any problem - in clay soil on a sunny slope. There are a couple of lavender plants in the same conditions that have survived for more than 20 years - I no longer have a record of what the variety is (Munstead maybe ) I think how they get pruned/cut back may play a big role in survival…!

What it always comes down to is your personal experience...so why not try it and see what happens. These are not super-expensive plants which take years to reach maturity., so you could take a few risks and see what works for you. Buy a couple and try them in different positions (and yep, protecting from winter rains can help, but there are many variables to consider.

I used to have a clump of some sort of lavender for something like 10 years, it always came back no problem (I was in zone 6 in the metro area at the time). At this house, I've had some not come back while some have, but the ones that have just never seemed very vigorous in their 2nd year so I ended up tossing them. My money is on it has something to do with the cultivar -- I have always maintained it's the older cultivars that are usually the tough survivors, newer cultivars bred for this trait or that just don't seem to have the same strength and vigor as the oldies but goodies, whether it's a lavender or something else. So seek out an old cultivar and you may find it just does fine as long as you give it what it wants -- which in this case is sharp drainage.

As far as other herbs, there are many that are reliably perennial. Chives, garlic chives, thymes of all sorts, oregano, and sage, to name a few. Common sage is quite a lovely addition to the perennial garden.

Phenomanal, Hidecote and Munstead lavender have all overwintered for me, no problem. After I dig the hole, I throw several handfuls of pea gravel at the bottom of the whole and I mix playground sand into the soil I'm adding back in.

I tried for several years to grow lavender with many different cultivars. Some survived some winters but those that did never thrived or lasted more than a few years. It's been my experience that lavender tends to look fine for most of the winter, with the very early spring being the most critical time for them. It seems like an early warm spell followed by a freeze (or multiple cycles of this) does them in quick. Maybe it is the fast temperature changes that are the cause of death, maybe it was because of snow melt or rain causing the soil to be saturated during those warm spells, maybe it is both. I really don't know. I tried growing them in the ground with gravel and grit added in, on raised mounds, in raised beds... Nothing seemed to work so I gave up trying.

Rodney

That’s just lavender itself, it has a short lifespan

I have seen some absolutely ancient lavenders. How attractive they are is a different question but 10 years is not an impossible ask and on my sunny allotment, there are clumps even older. I certainly have a few moving into their second decade of life (mostly the usual angustifolia such as Hidcote)...but I do have a somewhat mediterranean climate and soil conditions.