This is sheep's sorrel, Rumex acetosella.

It does look like one of the sorrels and they spread by both seeds and roots and are difficult to control. They do like a moist environment and grow faster in the mulched planting beds but do spread out into the drier lawn areas.
Control starts with getting the soil into a good healthy condition, well endowed with organic matter so the soil is well drained but evenly moist. Mow the grass high and encourage the grass to grow in good and thick and that should crowd out this plant.