Replenish + Lion's Eye Diamond

[Mulletus]

Can I pay for Replenish with LeD and get the enchantments from my hand into play?

[Windux]

You can't play the Replenish with LED.
You can jsut pop-up LEd, any time you could play an instant.
During the paying of a spell, you have no time to play an instant/ability, so you can't pop up the LED.

BUT if you pop the LED in response to the Replenish (payed with other mana), you get the Enchantments from your hand.

[iOWN]

And if you Burning Wish/Any Tutor and respond with popping LED, you can fetch Replenish and use the LED mana to pay for it.

Restating what Windux said: If LED was just a mana ability, you could announce that you are playing Replenish and sacrifice LED to get the mana (Replenish would not be discarded because it is entering the stack). But, it was worded to only be played as an instant - note: It still does not use the stack - so you can't use it during playing a spell or resolving a spell like you could with a normal mana ability.

edit - Fixed little error.