First I live in Charlotte

Traditionally my yard has been Fescue but it hasn't done well in the last couple of years.

The house faces south and in the dead of summer from the street back 20 feet gets baked.  Not even weeds grow some years.

I think that if I aerate, lime and fertilize and mix fescue with  another grass variety I won't have 20 feet of scrabble and dirt.

What should I plant?

The obvious answer might be to water heavily, but city water is EXPENSIVE.

Any recommendations for a grass variety that does well in direct sun and little water (depending on whether we have storms) and that I can grow from seed?

Your problem may be what's under the grass.

How thick is the topsoil underneath, or do you even have any? A good layer of organic topsoil is a must to having a nice stand of grass without having to constantly water red clay.

I cannot begin to tell you how many I see that have nothing much more than red clay and they cannot understand why they can't grow grass.

It's not the best, not the worst.

I've added soil over the years and mulched leaves and worked them in.

Back when I had a lawn service that dumped a ton of fertilizer and $$$ on it, it was a fair lawn most years, depending on rain.

Over the past 30 years, tress to our west have come down and it gets more sun than when we bought the house.

What makes most lawns look bad regarding sun is too little sun. Fescue and sunlight go together great.

Mulched leaves won't add that much, it takes more.

A good layer of at least 4" of topsoil is required at a minimum in order to maintain a nice lawn, 6" is even better. You also need to check the ph level as well. If the soil is acidic, you need to lime it to get a better balance suitable for the type of grass you want to grow.

Really good topsoil not only provides good organic matter, it retains moisture better as well. Clay will grow grass, you just have to water and fertilize a bunch. Really good topsoil smells, really smells as in organic material.

Get a good sample of your what your soil is and have it analyzed. It's not expensive and they can tell you what you need as far as ph and other minerals such as lime, nitrogen, etc . that you need.

I'm thinking about a mix of Bermuda and Fescue

Bermuda is brown all winter. The Bermuda will choke out the fescue. Those are really two different grasses as far as about everything.

Go to your local grass seed company or Farmers Co-Op. they will put you in the right direction and what you need. Without a good topsoil your results will be poor.

Anything is better than dirt and weeds.

And, I'm not sure where to find a farmers co-op in Charlotte

Seriously dude? You are using either a computer or smart phone to post, yes?

If you have a sun baked area, either Zoysia or a Bermuda will do well. They don't require much water, but I have found they need regular fertilizing (I use Milorganite, natural, and you can't burn your lawn with it).  A good prep for seed or sod is to spread some peat moss and top soil/cow manure and rototill it in.

Thank you

Zoysia sod is your answer.

Call your area co-op extension agent to have a look at your yard first and he-she will do a soil sample and give you the best recommendation.

OP, I’m in a similar situation with my house (Davidson, S facing) and fescue. I have no trees other than a small crape myrtle and my lawn gets POUNDED with sun come late June into July. The only way to make it survive is work your butt off preparing it in the fall, push it hard through spring with a full micro/macro program, and water deep & infrequently. I can keep my lawn looking pretty good through July but it definitely gets a little stressed unless I really water heavy (3x/wk).

Don’t waste your time trying to blend fescue and Bermuda. It will look funky then the Bermuda will simply choke out the fescue in 2yr.

Fescue is a high performance, high maintenance grass in the transition zone (CLT)
Warm season grasses like Bermuda are low maintenance and low performance (brown more than half the year)

You have to decide what level of effort you’re willing to put in and that includes what you’re willing to spend on water. It sounds to me like you want a warm season grass.

Don't mix bermudagrass and fescue....it will look like crap and you'll have to deal with bermudagrass, which is a PITA.

You need to over-seed fescue in addition to fertilizer and lime (IF it is needed).    Overseed in the early fall.

ETA- or just fertilize whatever junk comes up and keep it mowed tight.

I have the same problem with mud for a yard. I've got a bermuda "lawn" but it's so thin that it's impossible to let to dog out back without her coming in muddy. I desperately want a thick lawn. I don't care if I have to mow twice a week. I refuse to water more than once a week.
It's frustrating because back when I was in Illinois I spent nine years fixing the lawn there to have no weeds or bald spots. Now I get to start over from essentially nothing. I really want to sod over it, but expense is probably going to present a problem.

How long would it take to grow seed, lets say zoysia, from dirt if I till the whole yard and mix in a few inches of good soil? I'm thinking if I got done with that work in mid March- early April something could be established before the heat turns on...but I know nothing of when the heat really turns on and the rain turns off since I'm from up north.

The real  problem with a south facing lawn is water.  I forgot to mention the lawn slopes to the street so some rain runs off.

City water is EXPENSIVE.

Actually the water is reasonable but the taxes, fees, sewer charges and storm water run off is crazy.

My water bill last month, just for the two of was $77.

Imagine if I watered grass 2-3 times a week?

ETA:  That's why I was hoping to find a grass that tolerates sun and doesn't require a ton of water.

That is why you need topsoil. It retains moisture far better than clay. What also happens is that the clay hardens when dry sunny weather happens and when it does rain it mostly runs off.

I do this for a living.

I'm in Charlotte and will begin transitioning to zoysia this year.  The damn poa is driving me insane though. I just shot everything green with Round Up a couple weeks ago.  Pre-emergent is next for the areas I'm not plugging.

Once the plugs are in, I'm using Daniel's liquid 10-4-3 about twice a month from a hose end sprayer.  That worked great at my last house (not far from here).

we're in Indian Trail, same issue.  we've had luck with giving the fescue a lot of attention and plenty of water.  when we bought the place and treated, we watered heavy for a while.  the bill was....insane!

we're also in a subdivision type place so were constantly fighting the weeds from two neighbors and a common area behind us.

This is the very problem most have, you take the time, effort and money to have your yard look good only to have those around you let theirs go to shit.

Zoysia is great but it’s slow to establish.  
It’s definitely a pay it up front grass.  
If you can’t go the adding topsoil route, I’d suggest a soil sample box and send it to NCDA for analysis.  
You can specify zoysia as crop.  Report will tell you lime and fertilizer rates as well as micronutrient needs.

With clay soils, deep aerate and soil conditioner will help.

And zoysia can be combo plugged and seeded but it takes awhile to establish.

For y’all with utility yards like dog lots and such i would aerate and over seed with Bermuda.  Feed it and don’t mow too short.  2-3 inches and it’ll prob keep enough canopy thru the winter to not be so muddy.
Hope some of this helps.