It never rains but it pours

Solution 1:

Perhaps born under a lucky star

Very fortunate, as in Peter comes out ahead no matter what he tries; he was born under a lucky star.

Solution 2:

King James Bible, Luke 19:26

For I say unto you, That unto every one which hath shall be given; and from him that hath not, even that he hath shall be taken away from him.

As is often the case with such observations, the reason for this depends on who you are...

Poor person: "You're so lucky! You've had everything handed to you on a silver plate."
Rich person: "Quit whining! I make my own luck."

The idea that "luck begets luck" (i.e. - people who have been lucky in the past are more likely to be lucky in the future) is encapsulated in various idiomatic expressions...

hit a lucky/winning streak
be on a roll
be "jammy" - BrE slang, often applied to an undeservedly "lucky" person.

EDIT: I can't resist sharing this one, which sits alongside my "rich man" above...

The Harder I Practice, the Luckier I Get

As explained in that link, the origins are murky. No-one really knows when or how it started.

Solution 3:

"lucky things happen continually to lucky people".

neutral ones would be

you reap what you sow

you get out what you put in

Good things come to those who wait.

unrelated

Good things come in small packages

Best match

Good things come in threes.

The last one is probably the closest one I can come up with.

I.e. once lucky twice more lucky. And if you were lucky the last third time, what is preventing you from being lucky a 4th 5th and nth time?