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There is a new card called Bolas's Citadel which says:

You may play the top card of your library. If you cast a spell this way, pay life equal to its converted mana cost rather than pay its mana cost.

Can use my life to pay for any X spell?

No, you cannot choose any value for X other than 0 when casting cards using Bolas's Citadel.

The phrase "rather than pay its mana cost" or "rather than pay [card name]'s mana cost" is a standard phrase in Magic indicating that the cost specified is an alternative cost. This is stated explicitly in rule 117.9:

Some spells have alternative costs. An alternative cost is a cost listed in a spell's text, or applied to it from another effect, that its controller may pay rather than paying the spell's mana cost. Alternative costs are usually phrased, "You may [action] rather than pay [this object's] mana cost," or "You may cast [this object] without paying its mana cost." Note that some alternative costs are listed in keywords; see rule 702.

So if you cast spells using Bolas's Citadel's second ability, you are required to pay an alternative cost of life equal to the spell's converted mana cost. Then rule 107.3b applies:

If a player is casting a spell that has an X in its mana cost, the value of X isn't defined by the text of that spell, and an effect lets that player cast that spell while paying neither its mana cost nor an alternative cost that includes X, then the only legal choice for X is 0. This doesn't apply to effects that only reduce a cost, even if they reduce it to zero. See rule 601, "Casting Spells."

So, you are required to choose 0 for X when casting spells with X in the mana cost.