Both .laf and .ldb files are used by Lingoes translation software, yet for different purposes. It doesn't seem likely that one can be converted to another, except for the situation where you would backup your dictionaries and this would probably also cause you appendix files (.laf) to be saved in your backups (.ldb).
Convert Lingoes appendix file to Lingoes backup file.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert laf to ldb on Windows
A dictionary and text translation program
Convert from laf file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.