Your best bet for LIZD to JPG conversion is to use the program from which the .lizd designs originate the Live Interior 3D. It supports export to JPEG, probably for the purposes of 2D views. We haven't found information about any program 3rd party software that could work with Live Interior 3D formats.
Convert BeLight Live Interior 3D compressed design file to JPEG bitmap image format.
We have found one software suitable in our database for this conversion.
Apple macOS / Mac OS X software - convert lizd to jpg on OS X
A Home and interior design application for Mac
Convert from lizd 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.