When using DPM with log shipping if you setup DPM to protect your database and then add log shipping later, DPM does not automatically pick up the change and thus eventually will break the log chain resulting in a log shipping failure. DPM would then need changed and log shipping re-setup.
If you were to setup log shipping first then DPM will set itself up accordingly and the two can happily run together.
DPM and Log Shipping