No, he "obscured" to honor the king
Jeremiah had indeed made this very request of the king in a previous visit.
Jeremiah 37:15, 20 (NASB)
15 Then the officials were angry at Jeremiah and beat him, and they put him in jail in the house of Jonathan the scribe, which they had made into the prison.
"...20 But now, please listen, O my lord the king; please let my petition come before you and do not make me return to the house of Jonathan the scribe, that I may not die there.”
Is this lying?
No.
Honesty does not require us to tell all truth to all people, even including the truth that enemies would use to hurt good people. There is a time when the "honest" thing to do involves not giving full disclosure.
Proverbs 12:23 (NASB)
A prudent man conceals knowledge,
But the heart of fools proclaims folly.
Consider that with...
Proverbs 17:9 (NASB)
He who conceals a transgression seeks love,
But he who repeats a matter separates intimate friends.
...applied more widely by Petr...
1 Peter 4:8 (NASB)
Above all, keep fervent in your love for one another, because love covers a multitude of sins.
...And one last look at how much Mary didn't jabber on...
Luke 2:19 (NASB)
But Mary treasured all these things, pondering them in her heart.
...Our hermeneutical conclusion from this mini Bible-theo study on "honesty vs spilling our beans" is that there are surely times when wisdom knows when not to speak about a matter, and this strongly relates to love for others.
By telling Jeremiah to say that they talked about something they actually had talked about, the king is making a way for Jeremiah to not lie, while also honoring Proverbs 12 & 17.
This actually sets a Biblical model for "top secret" information in government.
Consider the situation (context)
This was a way to keep the city safe.
It is a time of invasion and siege. Guards suspect desertion (37:13). Soldiers are losing their trust from the public (38:4). There is no bread left in the city (38:9). The king fears betrayal from some of own people (38:19). People are being led out of the city (38:22). Everything is a security risk.
If word gets out that the king was actually considering a prophetic word to surrender to the invading enemy, the king himself could be regarded a traitor by the people and by his soldiers. That would make things even worse and wouldn't help anyone.
By being selective in his answer, Jeremiah allows the king to go about his decisions, which the king alone must make, without disturbing what little order is left in peaceful governance of the city.
Hermeneutics
On a hermeneutics site, "how we reached this conclusion" is the most important part of an answer. The hermeneutic we use here is about "connection".
When you read something that raises a yellow flag, research the background of the words. The king told Jeremiah to say something that raises eyebrows and makes us wonder what's going on. In that, he said something about "the house of Jonathan", so we should research to find what connection Jeremiah and/or the king had to "the house of Jonathan".
Don't make any conclusions—and don't start making explanations or excuses—before letting the context provide a response. Yellow flags call us to do research, not get theological. We may not even need to excuse lying or explain how even a prophet can lie sometimes. Perhaps, what happened wasn't even a lie, it just looks like one. "Quick to listen, slow to speak" from James 1:19 somewhat applies as our hermeneutic.
By doing research in the face of a yellow flag, we find that Jeremiah indeed had asked the same question the king told him to say he had asked.
So, the answer to your question is:
No, he obscured truth about a national-security matter to honor the king, to obey Proverbs 12, and to keep the people safe.
