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Your best bet would be to hand pull as much as you can and then add mulch to keep weed growth to a minimum. However, you could also try sprinkling corn meal in the area, which has a chemical in it that acts as a pre-emergent on plant seeds preventing them from germinating. Sprinkling corn meal will not harm plants but will keep weeds from growing. https://www.gardeningknowhow.com/special/organic/cornmeal-in-the-garden.htm

Another option (though not one I enjoy recommending) is the use of conventional weed killers. Most weed killers will dissipate after a certain period and that period will be noted on the packaging. Ortho Grass-B-Gon will kill weeds but won't harm your monkey grass.

Ortho Grass-B-Gon will kill weeds but won't harm your monkey grass.

It will, most definitely, survive over winter in your area. It will do ok in partial shade but it really likes the sun. They are drought tolerant to an extent, but I recommend keeping them watered regularly. If you have any other questions, please feel free to contact me here or at 6.schuster@gmail.com

You should definitely get all of the leaves off. You might even want to fertilize once per year in spring to get them started each year. Cutting them back several inches can also force them to spread. As far as mulching... You will want to do this after you cut them back. I don't prefer to use pine straw, but a good black mulch will be very good for them.

Here is an article for more information on Liriope: https://www.gardeningknowhow.com/ornamental/groundcover/monkey-grass/monkey-grass-a-spectacular-groundcover-for-the-lawn.htm

If the patch is manageable, then you can cut them all with shears. If it is too much for that, then a standard weed trimmer will be just fine. You really won't hurt them by cutting them down.

Can you include a photo? This could be many different issues from fertilization, to fungal problems. A photo, and a description of what led to the issue will help me.