I've been teaching leadership to junior officers and young businessmen for a couple of decades, and I always tell them the same thing I told my kids: There's no situation so bad that you can't make it worse by lying about it.
We want to lie because the truth is hard to say, maybe even hurtful. But truth is persistent, and it takes a lot of work to hide it forever. And your team knows most of what you know. When your lie becomes known, there are only a handful of outcomes, and all are bad.
People can choose to believe you just didn't know the truth. Now you look stupid or incompetent.
People can decide maybe you lied for a good reason. Now you're on probation; everything you say will be examined for the potential lie, because if you accept the idea of a good reason to lie, you'll find them everywhere.
Most likely, people will decide you lied to give you an advantage over them - you just played dirty. Good luck getting them to ever trust you again.
And that's the bottom line, as a leader. When you lie to your team, you're risking your ability to lead for a long time to come, maybe forever. It's your reputation on the line; without integrity there's no trust, and people don't follow leaders they can't trust.
Far better to say "I can't tell you," or even "I won't tell you." That will be scored as an honest response, even if they don't like it.
My preference: State the truth plainly the first time the topic comes up. It's like ripping off a Band-Aid -- being tentative isn't going to make it less painful.