Lungwort (Pulmonaria) is a shade-loving plant that thrives in a half-day shade or more, especially if that shade occurs during the hottest midday/afternoon hours. This bed appears to be receiving lots of light; is it in full sun? If it is, too much light can "bleach" and "sunburn" foliage and cause water stress, browning the leaf edges. More watering won't necessarily solve the problem because it's a function of the plant not being able to absorb and utilize the moisture fast enough to keep the leaves cool and hydrated, not necessarily too little moisture in the soil itself. If these plants are more shaded, then several other factors could be contributing to their struggles.

Lungwort requires good drainage and is not tolerant of over-watering or soils that stay damp. Roots cannot access enough oxygen to stay healthy in overly-wet conditions, and foliage may discolor and die off as a result as the roots decline and die. Root rot is not something plants usually recover from once it begins, but it may depend on how many roots were effected and if conditions change enough to cease decline. To avoid it, make sure the planting isn't being irrigated unless the soil feels like it's getting dry to the touch several inches beneath the surface, not including a mulch layer. (This goes for the established plants around them and the lawn as well, so it shouldn't interfere with the maintenance of other landscaping.) As a very rough guideline, in hot and dry weather this may mean watering once every week or two in clay-based soils.

If soil moisture is not the problem by itself, them crown rot or southern blight can kill plants (though these are exacerbated or encouraged by too much soil moisture), and various leaf-spotting fungi or bacteria can mar leaves (though won't kill the plant). It's possible more than one factor is overlapping in this case. Sap-feeding insects or mites are a possibility underneath some of the paler leaves, but you'd need to inspect them to see if any are present. Mites would be hardest to see but usually cluster near the main leaf veins. In general, though, lungwort doesn't have many pest issues and such damage can be selectively trimmed off. Using even low-impact insecticides in hot summer weather can be a challenge since they must be applied below a certain temperature, and treatment of the leaf undersides, necessary for good efficacy, is hard to do well.

For now, just trim off the worst of the leaves and keep monitoring the plants prior to watering rather than relying on an irrigation schedule. Even though some plants look a bit malnourished and off-color, do not fertilize, because ailing roots will not be able to absorb those nutrients and the influx could worsen their stress. (The health of the plants surrounding these supports the fact that the soil is not nutrient-deficient. Plants showing deficiencies typically have root health problems.) There is no need for a fungicide at this point, because once symptoms manifest or too much root damage has occurred, no treatment will be effective. If this is a fairly sunny area, move the plants to a shadier location (you can do this now and don't have to wait until autumn).

Miri

I think they are getting too much sun.