You have to consider the difference between external commands and built-ins. A built-in is a statement of the shell language, an external command is an external application which can run under any shell (if properly built). For example cd, echo, read are shell built-ins, whereas find, grep, awk are external commands. You can verify this using the type built-in:
$ type cd
cd is a shell builtin
$ type find
find is /bin/find
$ type type
type is a shell builtin
So you can run external commands - like lsb_release and uname - under bash or ksh indifferently. Furthermore bash and ksh are very similar in their syntax, whereas you will find more differences between the C-shells (csh and tcsh) and the Bourne shells (sh and bash). Other differences depend on the release: for example arrays were introduced in the Korn shell (ksh) earlier than the Bourne Again shell (bash).
In summary you have not to worry about using linux commands under a shell or another, you have to worry about the scripting language and eventually about the compatibility between different shells.