I would water the area thoroughly, and let it sit for a day or two so that it's not muddy, but the water should have soaked in. This will make it a lot easier to pull the weeds. Then go after the weeds near the flowers by hand, with a hand weeder. Pull all weeds within one foot of the flower plants.

The next step is iffy, because I don't know how big the area is. You can pull ALL the remaining weeds by hand or whack them with a hoe, or you can kill the remaining weeds with Roundup. The problem with Roundup is that it always manages to kill some of the good plants. So use a sprayer with low pressure, and spray very close to the weed, so that you don't get overspray and mist onto the good stuff.

Wherever you disturb the soil, you will likely find more weeds germinating in a couple of weeks. This is from weed seeds that were buried in the ground until you disturbed the soil surface. There are two ways to deal with this: hand-weed again; or, as soon as you are finished weeding the first time, put a thick layer of mulch over the whole area. This will keep light away from the weed seeds, which is the trigger that causes them to germinate. Mulch is also good for moderating soil temperature changes, in both hot and cold weather. So the lilies will like it, since hot soil is not good for them at all.

You mentioned that the area is steep. A coarse mulch, like wood chips, will control erosion during heavy rain and irrigation. Bark mulch can wash away if it's really steep. On a very steep slope, I would use a gravel mulch.

I'm not sure why you are rototilling. Is it for weed removal? If so, it will work, but you will be bringing up a lot more weed seeds out of the soil. Is it to prepare the soil for planting? If so, till deeply, then add soil amendments, then till them in. Then plant and mulch ASAP, to keep the weed seeds from germinating.

Depends on just how evil those evil weeds are - horsetail? blackberries? bindweed? A cultivated area that has been taken over by these types is difficult to reclaim without sacrificing smaller and more delicate perennials, so it may be best to relocate the perennials until the bed has been thoroughly purged of these weeds. This also allows the amending of soil after weed removal and the opportunity to redesign the planting area before replanting, perhaps adding other plants and groundcovers that will reduce further weed growth (bare soil = weeds).

If more traditional and less tenacious weeds have invaded, manual removal should suffice. A good soaking the night before will allow easier removal. You can also cover the weedy areas with dampened newspapers (don't skimp, use a good thick layer) and then cover the newspaper with an organic mulch.

RoundUp in an area planted with perennials would be my last choice - damaging or killing the existing plants is pretty much inevitable.

If she just moved in and hasn't seen a whole year, there might be things dormant that would be worth saving from the rototiller.
I have found it easier to work in smaller more manageable sections. There is no point weeding the whole area if she is not able to plant and mulch it afterwards as well- or keep it covered until she does. I have many times had ambitions of reclaiming an area, only reclaim it over and over again because the weeds come back when I didn't have time or energy to finish.
Pull off flowering/seeding stalks to keep new weeds to a minimum. Also, re rototilling- you sure wouldn't want to do that around bindweed, buttercup or the like.
Good luck to her.

Flower beds are for those with a good supply of elbow grease.

I, too, have some intimidating bushwacking ahead of me. My suggestions to her are:
Decide what type of yard you would like, and what your maintenance level is (including watering options).
Only do a portion at a time.
Mulch, mulch, mulch! :-)

That's weird: I've always found it much easier to pull typical little weeds or tufts of stray grass out of very dry soil, rather than wet. My garden soil is largely sand, lots of compost.

I wouldn't rototill for several of the reasons cited: killing hidden unknown plants, digging up weed seeds and, number 3, it's on a steep slope. Those monsters are hard enough to handle on flat land! A hula hoe with the D- shaped flexing head are really fast and quite easy to handle.