You can use the -I option together with the -i, -o, and -e options of bsub to selectively redirect streams to files. For more details, see the bsub(1) man page.
% bsub -I -q interactive -e job.err lsmake
If in your environment there is a wrapper around bsub and LSF commands so that end-users are unaware of LSF and LSF-specific options, you can redirect standard output and standard error of batch interactive jobs to a file with the > operator.
By default, both standard error messages and output messages for batch interactive jobs are written to stdout on the submission host.