You cannot save a variable for later use in other Dockerfile commands (if that is your intention). This is because each RUN happens in a new shell.
However, if you just want to capture the output of ls you should be able to do it in one RUN compound command. For example:
RUN file="$(ls -1 /tmp/dir)" && echo $file
Or just using the subshell inline:
RUN echo $(ls -1 /tmp/dir)
If you have an actual error or problem to solve I could expand on this instead of a hypothetical answer.
A full example Dockerfile demonstrating this would be:
FROM alpine:3.7
RUN mkdir -p /tmp/dir && touch /tmp/dir/file1 /tmp//dir/file2
RUN file="$(ls -1 /tmp/dir)" && echo $file
RUN echo $(ls -1 /tmp/dir)
When building you should see steps 3 and 4 output the variable (which contains the list of file1 and file2 creating in step 2). The option for --progress plain forces the output to show the steps in later version of Docker:
$ docker build --no-cache --progress plain -t test .
Sending build context to Docker daemon 2.048kB
Step 1/4 : FROM alpine:3.7
---> 3fd9065eaf02
Step 2/4 : RUN mkdir -p /tmp/dir && touch /tmp/dir/file1 /tmp//dir/file2
---> Running in abb2fe683e82
Removing intermediate container abb2fe683e82
---> 2f6dfca9385c
Step 3/4 : RUN file="$(ls -1 /tmp/dir)" && echo $file
---> Running in 060a285e3d8a
file1 file2
Removing intermediate container 060a285e3d8a
---> 2e4cc2873b8c
Step 4/4 : RUN echo $(ls -1 /tmp/dir)
---> Running in 528fc5d6c721
file1 file2
Removing intermediate container 528fc5d6c721
---> 1be7c54e1f29
Successfully built 1be7c54e1f29
Successfully tagged test:latest