The phrase every silver lining has a cloud, or its cloud, also there is a cloud to every silver lining, means that every comforting or hopeful situation has a sad or unpleasant side to it, even though this may not be immediately apparent.

This phrase is of course a pessimistic reversal of every cloud has a silver lining, or its silver lining, also there is a silver lining to every cloud.

The earliest occurrence that I have found of this pessimistic variant is from Words of Wisdom, published in The Chesham Examiner, Amersham and Rickmansworth Times (Chesham, Buckinghamshire) of Friday 18^th May 1900—but the fact that the phrase appears among several hackneyed ideas may indicate that it was itself already a cliché:

Smooth sailing does not make skilful sailors.
There are cases where it is best not to be wise.
Trifles become troubles because we trifle with them.
A man may be measured by the subjects of his mirth.
Every man has sufficient cunning to deceive himself.
Thought is the bud, but deeds are the ripened thought.
Some people persist in seeing a cloud to every silver lining.
You can learn nothing of a trifler, unless it be the folly of a vacant mind.
[&c.]

The phrase then occurs in a letter on “clergymen who have risen”, by “a ploughman poet-rector”, published in The Yorkshire Post (Leeds, Yorkshire, England) of Friday 12^th September 1902—in this case too, the fact that there is a cloud to every silver lining immediately follows the trite phrase all is not gold that glitters may indicate that it was already a stereotype:

When a ploughboy does become a parson, and even a poet, all is not gold that glitters; and there is a cloud to every silver lining! If ploughmen are wise, unless they have particular friends indeed, they will stop where they are.

The third-earliest instance of the phrase that I have found is from To-day’s Gossip, published in the Sunderland Daily Echo and Shipping Gazette (Sunderland, County Durham, England) of Friday 13^th March 1914:

Mots of the Moment.

The truth will not last any longer if you stretch it.
The trouble is that every silver lining has its cloud.
Every man has his price, but some men give themselves away.
A man is never very reliable when he tells how badly his tooth ached.
We never heard of a bride that wasn’t vivacious, dainty and charming.
A new hat is to a woman what a new dog is to a man—something to talk about.

The phrase has probably been independently coined over and over again in the course of time. This is illustrated by the beginning of Every silver lining has a cloud!, by Jan Van Embden, published in Bray People (Bray, County Wicklow, Ireland) of Friday 28^th July 1989:

Time was when the expression “every cloud has a silver lining” was top of the list of favoured sayings for any self-respecting optimist.
Of late though, there’s been so much silver lining around in the form of weeks of blistering Mediterranean-like weather that pessimists have begun to paraphrase the motto to “every silver lining has a cloud”.
And for some local traders around Bray, that’s been a very apt expression as the glorious heatwave has hit their business.
For while the weather has been a godsend for some obvious beneficiaries like the tourist trade, ice cream sellers and the hawkers on Bray Seafront who sell everything from buckets and spades to candyfloss, the blue skies and high temperatures has spelt real trouble for others.