If I were bidding on it, here's what I'd do:
1. Tell them everything. Explain your concerns.
2. Suggest that they start with just mowing the weeds, front and back. Very basic package. I'm always amazed at how good a patch of weeds looks after mowing it for a month. Get them a decent hose end sprinker and a simple timer, and teach them to use it. It's not a golf green, but it's not weeds. Once the lawn gets used to being mowed regularly at 3 inches or so, ask them about a broadleaf herbicide treatment.
3. Get the irrigation system working.
By the way: won't a slit seeder wreck the sprinkler heads? Maybe mow for a year, then in the fall on a day of light rain, seed and roll. The Briish have been doing that for 300 years. You have to use more seed when you do that, but you save the price of the rental on the slit seeder. And if you have a working sprinkler system, you can set it to run often enough to keep the seedling grass moist.
4. Ask them what they want in an ideal world, what their budget is to get there. Some of it is ongoing, some is once only.
5. Talk about xeriscaping -- moving to a no-mow solution. This has tremendous appeal for lots of people, particularly in cities where water is rationed. Still requires periodic maintenance, mostly vacuuming up leaves and needles, or massive gardening, depending of whether they have beds or cover with gravel.