You may both need to do a bit more than just feed the lawn. If you inspect below the blades of grass you will probably see a mat of brown, dead grass along with a bit of moss etc. This is 'thatch' and needs to be raked out to stop it throttling the grass that's trying to grow through it. This can either be done by hand with a lawn rake or with an electric scarifier / cylinder lawn rake. Don't worry if you pull out some live grass at the same time, it resilient stuff and will grow back. Once you've cleared out the thatch, leave the grass for a week or so to recover a little and then cut and feed as normal.