The case against Lugovoi seems to be pretty strong in the sense that Lugovoi was the only person whose whereabouts in London most closely (though far from perfectly) coincided with the Polonium traces. The motive is not clear, and the British government didn't (and probably couldn't) clarify it. Most of the Western media mistakenly labeled Lugovoi "a former spy," just as they labeled Litvinenko. In fact, the last time Lugovoi was associated with secret services was in the early 90s. After that, for the most part he was Boris Berezovsky's man, responsible for the oligarch's security. After Berezovsky's exile, he maintained friendly relations with him. He even served time in Russian jail for helping another of the Berezovsky's associates - Nikolai Glushkov - escape from detention and flee abroad. Nevertherless, Lugovoi retained good relations with both Berezovsky's entourage and the Russian elite.
It is unlikely that Lugovoi and Litvinenko had any business dealings. Lugovoi is a fairly rich businessman; his worth is estimated at tens of millions of dollars. A job as a simple gun for hire would hardly appeal to him. Litvinenko, on the other hand, was nearly penniless, a fish out a water in a foreign country, without command of the language, living on an allowance paid by Berezovsky, who gradually cut Litvinenko off because he became more of a nuisance than an asset.
The official British version was somewhat implicitly challenged by Julia Svetlichnaja, a 33-year old Russian grad student at the University of Westminster. In a series of articles in the British press, she described her meetings with Litvinenko several months before his death. She wanted to contact Chechen exiles in London for her disseration work and thought that Litvinenko could help her. She was struck by Litvinenko's erratic behavior, his carelessness and paranoia, his endless rants and his innumerable conspiracy theories. She implied that Litvinenko was more of a danger to himself than a target of a big conspiracy. In particular, he blabbered constantly and openly how he was going to blackmail rich Russians, both in Britain and back home, with dirty secrets he allegedly had on many of them. He also grabbed at every possible conspiracy lead, no matter how ridiculous it looked.
I find Svetlichnaja more believable than others, if only because I know her type. The British press accused her of being an instrument in the Kremlin campaign - but they couldn't back up their accusations with evidence. Svetlichnaja even won a libel suit against The Sunday Times. Rather than being the Kremlin's instrument, she was more probably just pissed off by the xenophobic hysterics of the British press that treated every Russian expat as a criminal or a spy.
It is a very tragic story, considering the horrible, painful way Litvinenko died, but I can't help laughing at how many ridiculous, comical characters are associated with it. Take, for example, Mario Scaramella - the Italian guy who ate lunch with Litvinenko at the Itsu sushi bar around the time of his poisoning. According to Litvinenko, the Italian brought with him a bunch of documents he claimed were of crucial importance. But even Litvinenko, a big conspiracy buff himself, found them mostly useless, and saw no reason why they couldn't just have been emailed to him.
Scaramella claimed to be alternatively a "security expert," a university professor, a secret service agent, a police inspector, and so on, apparently without any real credentials. He was convicted for fraud and is now under investigation by the Italian police for weapons smuggling (in a case separate from Litvinenko's). He was associated with the "Mitrokhin Commission" of the Italian Parliament, headed by Paolo Guzzanti, a close friend of Berlusconi and the member of the right-wing "Forza Italia." The apparent purpose of the commission was to "out" Romano Prodi, Berlusconi's political rival and the current Italian PM, as a "KGB agent."