The lawn is lacking in nitrogen, so in order to have a green lawn you need to feed it with a Nitrogen based fertiliser, in the UK we use a commercial fertiliser called Evergreen, which also contains a weedkiller that gets rid of most annuals. The effect doesn't last long though and needs to be repeated about every six weeks.
A more long term solution is to top dress the lawn in the spring, this is quite a job, but the results are fantastic.
First you need to rake the lawn vigourously with a spring tine rike, this removes all the dead thatch and moss, after that the lawn need to be spiked, this is best done with a hollow tine tool, it removes small plugs of earth about 10mm in diameter and about 50mm long, this relieves compaction and also allows water to get to the roots.
You then need to top dress it, you do this by adding grass seed to a good fine commercial multi purpose compost, and spread it all over the lawn, brushing into the holes made by the tines. Then water well, if the weather stays dry you will need to water twice a day.
After a few weeks your efforts will be rewarded with a thick green lawn, worthy of any golf course.
Other tips are :
Do not be tempted to cut grass too short, unless you can afford to water really well on a daily basis.
Despite what lawn mower manufacturers tell you, use a grass collection box all the time, a lawn does need a lot of mulch.
If it is an ornamental lawn, next time you buy a mower, buy a cylinder mower, it's better to cut grass like using a scissors, than trying to slash it with a spinning knife !