A lot of this is informed by statements the OP has made in comments, which gives more insight into the question.
1) lots of complaining about the lead going on leave when there are "time sensitive issues"
In my experience there is never a "good" time to take leave. Can you really anticipate a time when things will be "slow"? No. I don't think you can. So when can he take his vacation?
2) lots of complaining that he has not helped you find a replacement lead to cover while he is away.
As others have pointed out, you are in the position to ask for substitute or additional resources. He is not. I don't understand what you don't understand about this.
Additionally, I'm not sure why you think a temp lead will help. Even on a long term basis, very often you can't simply throw people at a scheduling problem to secure the desired effect. But especially on a short term basis, to cover someone who is on vacation, by the time the sub is up to speed, the lead will be back. This solution makes little sense, IMO. And in any case, it's your responsibility to make this happen, not the team lead's.
Finally, on the topic of leave in general, did it occurr to you that the lead may be "underperforming" precisely because he actually and in fact needs some time off to avoid complete burnout?
3) lots of complaining that the lead is not performing his tasks as "required".
You have not thoroughly explained what these tasks are, but from comments it sounds like you have set up extra requirements for the lead and team members which seem to support giving you a view into what they are doing, at the expense of them actually getting work done. In short, this sounds like micromanagement diguised as a "productivity enhancer". It's not. It rarely is.
A group of three people simply do not NEED to coordinate their tasks via jira to achieve a level of teamwork amongst themselves.
You commented that it is in their best interests to update jira (by hand?) to keep you from bugging them every 10 seconds to find out what they are working on?! No. Just no. That is just not effective management. They have presumably been working together long before you arrived so let them do their thing, and find a different way to get status updates that does not rob them of precious development time.
The other specific "task" that's mentioned is that the lead is not keeping up to date with the project planning software. Again I have to suggest: it's your job, as the project manager, to do this kind of paperwork. Why are you having him do that, while at the same time complaining that the actual deliverable, which he can actually contribute much more to, is slipping?!
I'm sorry to be harsh about all of this, but this whole thread gives me flashbacks to the worst boss/PM I've ever had in my life. We would keep her informed of any risks, she would ignore us and tell management everything was "green". When the risks came to fruition and things started to slip, she would start piling on extra "tasks" that were supposed to keep us "on track". She would also schedule extra meetings to discuss what was going on, to "stay on top of things". She constantly interrupted our work and made it even more difficult for us to reach our milestones. She basically robbed us of valuable time that we could have spent finishing the deliverables, and filled it with nonsense busywork that basically gave her more rope with which she then tried to hang us, to management.
Which of course quickly extinguished any fire left in our bellies to forge ahead and do everything we possibly could to make it work.
I mean, why bother?
My overall take is that you were not hired to be a real PM, but to serve as a human stick. You will not "win" this battle by rolling over and alienating your team by trying to beat them down. There is so much good advice here. Stop responding with "but he..." and focus on what you can do to implement the treasure trove of excellent answers here.