Sometimes, you need to change the unit cost of a job, but just for one job. Your next jobs for this client will have to be invoiced at your 'normal' rate (the one you defined at the client level, under People > Clients > Services tab of the client).
There is a way of managing this in LSP.expert.
If you don't need any details on your invoice (no matches, no wordcount), you can use the 'Fixed price' field in the job to define the one-off price of your job.
If you do need details on your invoice:
You create the job normally, and the system will automatically calculate the price based on the rate you defined at the client level.
You create a quote for this job (even if your client didn't request any quote) by clicking on Create > A quote in the job (see screenshot above).
In the quote you just created, you can adapt the price as you wish, based on what you agreed with your client. The fact that you link a quote to the job will "lock" the price of the job, without affecting your next jobs for this client and without updating your rate at the client level.
Please note that the price of a job is "locked" only when the status of the linked quote is Created, Sent and Accepted. If the quote is marked as Rejected, the price of your job won't be "locked" anymore.
WARNING: changing the price of a job directly in the job (on the left in the job details) automatically updates what you defined in the client's details. So the estimate of all your uninvoiced jobs will be updated based on the new price you defined in the job.