Yarrow can survive long periods of drought, it spreads by underground runners and seed.
Once established it can spread quickly and it also tolerates close mowing.
Leaves - Yarrow has feathery, fern like leaves that give off a fragrant smell when they are crushed.
Flowers - The flowers are a white or pale colour and form on the end of stems in dense clusters. Yarrow flowers between June and October.
Roots - Yarrow has a fibrous root system with many rhizomes which help the weed establish and spread.
Habitat - Yarrow prefers soils that are dry and deficient in nutrients. Yarrow is often a good indicator of nutrient deficiency (low fertility).
Cultural Control - Yarrow can be physically removes by hand weeding taking care to remove all of the roots. Regularly mowing the lawn will help stop the weed producing seed heads.
Raking the weed prior to mowing will help stand up the lateral growth and weaken the weed.
Ensure the lawn receives adequate nutrition as this will encourage a thick lawn and help prevent any Yarrow problems.
Chemical Control - Yarrow is going to be difficult to control using chemicals as it is resistant to many selective weed killers.
If go down the chemical route choose a product that contains 2,4-D & mecoprop-p or 2,4-D & dicamba. Repeat applications will be needed and success may be limited.
Alternatively you may want to call in a professional lawn care specialist with the relevant pesticide application certificates.
They may have access to professional weed killers used in the sports turf industry. These are more effective than the weed killers that are available to the amateur gardener.