I think a large part of luck works in the opposite manner, although I don't think the claim you're making is the same claim that the Telegraph is making (indeed, I'm not sure if the Telegraph is saying anything specific enough to count as a claim).
Suppose you always do things that have a 95% chance of working, but don't have a high payoff. You apply to safety schools for college, you only date people you already know really well, you get a safe, steady job that pays a respectable salary, without much danger of getting fired or outsourced. You'll probably think, "Wow! 95% of the stuff I try works! I must be really lucky!"
Now, suppose that you always do things that have a 5% chance of working, but do have a high payoff. Say, you try to start five different companies, and all of them fail. You'll probably think, "Wow, I must be unlucky, nothing I try works", and it's quite possible you'll just give up, even if one success would make you worth $100M.
You're basically saying that risk-averse pessimists call themselves lucky and optimistic risk-lovers call themselves unluckly. This makes sense; when someone calls themselves "(un)lucky", they're really referring to their incorrect calibration.
On reading the article, the takeaway message seems to be that the 'unlucky' systematically fail to take advantage of high-expected-but-low-median value opportunities.
Actually, the article says:
Unlucky people often fail to follow their intuition when making a choice, whereas lucky people tend to respect hunches. Lucky people are interested in how they both think and feel about the various options, rather than simply looking at the rational side of the situation.
Wiseman's use of "rational" doesn't really mean the same thing as we use it to mean around here, of course. A full reading of the article suggests that he means something more like "cerebral" or "singularly focused", just as by "intuition" he means openness to subconscious information.
Or to put it more simply, lucky people make use of System 1 (which can respond in parallel to a wide variety of possibilities), as well as System 2 (which is extremely narrow-focus and serial by comparison). This also offers a ready explanation for the common "intelligence equals unhappiness" meme -- people who've highly developed their System 2 skills to the exclusion of their System 1 management/awareness skills are going to be unlucky, and thus unhappy.
Now, we could question whether System 1 is also biased towards the sort of thing you're talking about, but a big point of the article is that unlucky people never even notice things that the lucky people do. So, it really isn't a function of conscious payoff consideration, at least not in the newspaper and dot experiments described. There were no payoff considerations as such, even if the practical effect was one of limiting payoff opportunities by maintaining a narrow focus. There might be a correlation between those things -- i.e., risk aversion might certainly encourage a person to develop S2 at the expense of S1 -- but once that commitment has been made, the person's going to stay unlucky even if they change their mind about payoff probabilities in general. (Unless, of course, they develop the S1-management skills described in the article.)
Perhaps the causality is backwards here. If a person believes they're systematically unlucky, then they would incorrectly expect to do worse on high-variance bets than the expected value would indicate.
It seems reasonable that people who exceptionally report themselves as "unlucky" tend to have actually had worse outcomes than they deserve (obviously if a trait that causes people to fail also causes them to excessively claim "I'm unlucky", then that need not be true). But suppose it's true; then to the extent that excessive pessimism leads to self-sabotage, just the right amount of feel-good keep-trying brainwashing will undo the damage.
As for people who are optimistic already, I see no reason to encourage them further. The "training" that succeeded in making lucky-feeling people feel even luckier probably had no further performance benefit.
In general, if you tell someone they're great because of some trait, they're likely to conform to that expectation or at least self-label with it.
From the UK Telegraph:
Be lucky -- it's an easy skill to learn
On reading the article, the takeaway message seems to be that the 'unlucky' systematically fail to take advantage of high-expected-but-low-median value opportunities.