Lloyds did manage to get into significant financial trouble in the mid 1990s leading (surprise) a lawsuit and eventually to a substantial restructuring of its business practices.
from the wikipedia article:
The 'recruit to dilute' fraud allegations were heard in court in 2000 in the case Sir William Jaffray & Ors v. The Society of Lloyd's (see first instance judgment) and the appeal was heard in 2002. On each occasion the allegation that there had been a policy of "recruit to dilute" was rejected; however, at first instance the judge described the Names as "the innocent victims [...] of staggering incompetence" and at appeal the court found (see appeal judgment) that representations that Lloyd's had a rigorous auditing system were false ([item 376 of the judgment:] [...] the answer to the question [...] whether there was in existence a rigorous system of auditing which involved the making of a reasonable estimate of outstanding liabilities, including unknown and unnoted losses, is no. Moreover, the answer would be no even if the word 'rigorous' were removed.)