The Daily Mail may have acted bravely on the Stephen Lawrence murder, but they have also acted very badly indeed in (countless) other situations.
It has a recorded record of damaging people. The rich, famous or powerful can sue and fight back, but the others? Your average Joe? An ordinary person hung out to dry by them? Or humiliated by them? Or the countless women shamed for getting fat, or aging, or just simply committing the sin of living while female.
In terms of Dame Lawerence - for me personally I cannot impose on her an expectation of behavior. I cannot imagine, not even for a second, how I would be if I had to go through what she went through.
She gets maximum compassion, and a pass from me.
In terms of the Daily Mail - I mean, it is owned by a very powerful player, it wins some and looses some. I don't really see it as a "moral" player at all, in the sense that it seems to only be there for the class interests of the owners, and in the main, sells clicks and papers by degrading others. I really cannot be upset on its behalf, morally or otherwise, in this one situation. It has enough money, strength and power to look after itself, and is not a decent enough publication to be rooting for it.