Yes, you can invoice a job based on the time you worked on it thanks to the time tracking functionality in LSP.expert.
You have to select the Time-based invoicing option for the job concerned. You can do that before beginning to work on the job, or afterwards.
Once you finished the job and you have all your time tracking entries in the Time tracking tab of the job, you have to define these entries as Billable (by clicking on the red cross next to each entry).
The system will add up all the billable entries and this total time will appear on your invoice (you can modify it manually in the invoice if you want).