Get what back? If you mean Lightroom, yes you can install it with your serial numbers. If you mean your catalog and photos, you will have had to be making backups on an external drive.
I don't speak english very well, so I don't quiet understand the end of your andswer.
but I can precise : what I want to get back is all my pictures ! are there lost or is there a way to get them back ?
thank for your answers !
I hope I'm not being confusing. Pictures are stored as computer files. If your computer is lost, did you have copies of the files on another disk?
If you are asking about installing Lightroom on your new computer, you can. Do you have a record of the serial number?