What are some of the best, cheap sedans to lease right now?

Toyota Corolla, Mazda 3, Nissan Sentra, or the Ford Focus would all be good choices.

You could move up to the Camry, Altima, 6, or Taurus, but that depends on how important price and gas milage is.

Why lease? I know it’s off topic but you can go into a new car dealer and get a leftover from last model year with special incentives. While a lease may or may not have a special monies to apply to the cost. Also after paying for 3 years all money is gone and there is no trade-in value only monthly receipts.
I second @DeanV‘s choices, if five passengers is a MUST you have to go with the Camry, Altima or Taurus ( bigger back seats ).

If she really needs five passenger, I’d go with a Honda Accord.

I have a 2011 Accord Sedan SE and I can get on a full tank 500+ miles highway, and 400+ city/hwy on the 20 gal. tank. I may be low balling my results as the car does exceptionally well on fuel. In fact, I’ve had the car since August 2011 and I have run up over 22K miles on it.

It is good, but not great on passenger room; trunk space is very good as well.

Rented a Ford Focus four-door on a recent trip and was impressed.
Good mileage, good power, good headroom, good seats, big trunk, stable, practical.
The rental had a fancy-pants package including a nice sunroof, power windows – and both-sides power mirrors which is great for multiple drivers.

The newest model is a bit bigger than previous, and I think it could fit five passengers with no problem.
It was parked close to a Focus that was one or two years old and clearly has more passenger room than the older one but does not have a much bigger footprint… it’s mostly a bit taller and more filled out.

If I had to replace our car now the Focus sedan would be on my short list easily.
(But the old ‘96 Saturn SL2 sedan shows no signs of giving up the ghost at this time with 30+ mpg still).