Yes, you can.
The LGPL allows you to use a library (in this case the library which interfaces between your program and the PostgreSQL database server) as a dynamically linked library in any software for any purpose and distribute the program under any license, as long as you follow the attribution requirements explained in section 4 of the license text and don't change the library itself.
If you did make changes to the library (I hope you didn't, because this is something a programmer should generally avoid for various reasons), you need to release your changed library together with the application under the terms of the LGPL (which means with sourcecode).
But even these conditions only apply when the company you made the program for decides to sell or give away the program to third parties (or in the language of the GPL: "conveys" the program). As long as it is only used internally and never leaves the company, you can ignore pretty much all requirements of the LGPL.