[BiglyCommentary]

Yes there was a condition

No there absolutely was not. But feel free to point where it was in the exact word spoken:

"Thus says the Lord: Set your house in order, for you shall die, you shall not recover."

[Olog-hai]

If there was no condition, then God would not have rescinded the prophecy in spite of Hezekiah’s prayer. But as Isaiah 38:4-5 says:

Then came the word of the LORD to Isaiah, saying: / “Go, and say to Hezekiah, ‘Thus saith the LORD, the God of David thy father, I have heard thy prayer, I have seen thy tears: behold, I will add unto thy days fifteen years.’” …

Clearly a different prophecy from the former, which was rescinded.