LLA is library lookaside. These are programs, such as the linklist, loaded by the operating system into memory for rapid access and, depending upon how the site is configured, may include other libraries.
Using an LLA library is NOT required for a COBOL - DB2 program nor for a simple COBOL program -- ever. Your site, however, may have placed your COBOL / DB2 load library into the linklist for performance reasons in which case an LLA refresh would be required after compiling the program before the new version would be used -- but this depends upon the site. The DB2 installation process typically places some system load libaries into the linklist, but application program load libraries may -- or may not -- be placed in the linklist, depending upon site standards and procedures. So, basically, the answer to your questions are -- follow what your site tells you to do. If your site has you compile into linklist load libraries, you will need an LLA refresh; if your site doesn NOT have you compile into linklist load libraries, you will NOT need an LLA refresh.