The two main problems for a lawn - are moss and weeds.  There are treatments for both - but without addressing underlying causes the fight is futile.

For moss - in spring or autumn open up the structure of the lawn all over with a fork or aerator.  Remove as much moss as possible with a de-thatcher.  Introduce some sand or top soil and brush into the fork holes of the lawn.  Over-seed the entire lawn in spring or autumn.

For weeds - only an inorganic weedkiller is able to tackle a weed infestation effectively.  For an organic solution - cover the surface of the grass with a thin layer of topsoil.  Over-seed onto this topsoil.  In most cases the weeds arrive because there is insufficient grass coverage - to deter weeds - so regularly over-seed.

Feed your lawn with chicken manure in spring - yes chicken manure.  This will promote an organic alternative, promoting healthy grass growth and reducing moss somewhat.