With this question, I would like to shed some light on the Lion's Eye Diamond card, and some of its possible uses. It is an incredible card, which in some ways is similar to the Black Lotus, but which unfortunately cannot be completely associated with it, for obvious reasons.
First, it is possible to note that the Oracle card text and the original card text are noticeably different. At first glance, it would seem that the only current use for this card is the ability to use the three mana for some activated ability of the cards that are already in play.
In fact, I think I can exclude the possibility of "starting to cast a spell". With this last expression, I mean in the sense that, having chosen a spell from the hand, and with the Diamond already on the battlefield, you can cast it thus excluding it from the hand – and thus sidestepping this way the wording "discard your hand" as regards the spell you would cast with the help of the Diamond.
In other words, I don't think it's possible to use this card as a mana source anymore, and with the rules associated with mana sources only: this is also because, unlike the original text, Oracle says that the ability of this card can now only be played as an instant.
But even this use seems really strange to me ... Before the errata, it was a mana source, and now, even if it remains largely such, it must be used as an instant ... There remains, in my opinion, no other possibility of using this card for the activated abilities of the cards already in play.
I would want to know if what is reported here is correct, and if any expert – or, who has ever played with this card – has any idea how it can be used differently from the way shown here.