What type of grass is it? Do you have pictures of the overall area? Some grass types die in the summer heat and do a poor job of spreading/repairing themselves. These grasses need to be overseeded every year or they get progressively worse. Other grass types do a better job repairing themselves if cared for well - but may take some time.

From what limited info I can get from the few pictures provided I can see:

1. water competition near tree, much beds, high spots.

2. greener grass in gullies and low spots

3. competition for resources with weeds

4. lots of cut grass on the lawn

5. disease/brown patches in what could be low areas surrounded by darker green grass

For 1 & 2 changing your irrigation may help. If you know how much water each area get, you can compensate to even things out. For 3, using a pre-emergent year round would help that issue - it's expensive but well worth it imho. How high do you mow, 3"? 4?" When do you mow? It look like the mowed grass layin on the lawn is about the same height as the grass it is laying on. In that case it means you are mowing 50% of the grass off at a time. You should only mow off 1/3 MAX. So if your grass is 3" tall it should be mowed BEFORE it reaches 4" to be safe, esp with high & low spots. Letting your lawn get to 4.5" will give you a little bit more time before you have to mow it at 6". Plus the lawn with shade out many weeds, required less water, etc. The grass also needs to be mulches, not just side discharged and left to lay there. The piles of grass take much longer to decompose and become hotspots for disease.