Malva, also known as mallow or cheese weed, can definitely be difficult to manage.
Here is some general information out of UC Davis that might be of interest: http://ipm.ucanr.edu/PMG/PESTNOTES/pn74127.html
Hand weeding is an alternative to mulching. Any weed removal should be followed by taking steps to improve the quality of the lawn so it is more competitive against future weed invaders. OSU has several publications on lawns that cover restoration and good management practices: https://catalog.extension.oregonstate.edu/ec1550
Malva is difficult to control with herbicides and may require multiple treatments in the spring. Some 2,4-D based products are labeled for home lawn use. Please use caution when using pesticides and throughly read the label for an special precautions before applying.
Hope this helps and thanks for using Ask An Expert!