If you don't know why P isn't confirming L, something is really wrong between you two. I know that can happen in a workplace. Perhaps you work for a vendor to the company that P works for, and have no leverage at all.
If you want P to confirm L in writing, but P is not doing so, then you need to find a way to do one of these things:
- make P want that too.
- establish why P isn't doing it, and clear away that problem so that P can confirm
- get yourself free of the need to confirm L in writing
One of those three will get you where you need to be.
Since you haven't told us anything about your relationship, or what L is, it's hard to know how you might do #1. You need to say something to P like:
- until you confirm L, I can't keep working on your project, even though you are a paying client of mine (or of my employer).
- if you don't confirm L by Tuesday, I am going to take this as constructive dismissal, stop coming in to work, and proceed with a claim of unfair dismissal.
- if you don't confirm L by Tuesday, I will not marry you and I will call all the vendors to cancel everything we have booked
- until you confirm L, I will be unable to move forward on this project at all and will have no billable work to do. I will work on nonbillables as much as I can so that the salary you pay me isn't completely wasted
- until you confirm L, I will not move to your city and start working for you
- If L is not confirmed by Tuesday, I will start applying for jobs elsewhere. If I find one before you confirm L, I will take it and give you two weeks notice at that time.
- My manager agrees that if you do not confirm L by Tuesday, the project will be cancelled and we will be sending an invoice for our time spent so far. There is also a possibility of legal action to recover some of the lost profits as a result of your refusal to enable the project to proceed.
And so on.
You have to find a way to make P want to (or be able to) confirm what you need confirmed, or find a way to remove your need to have it confirmed. Those three things are within the realm of the possible. Putting magic words in an email that "force" P to confirm L is not within the realm of the possible. So either find a way to motivate P, or find a way to live without the confirmation. Those are your only options.