Can I claim PDUs for presentations or lectures from providers which are not PMI R.E.P.s?
Yes you can. The important question to ask yourself is not "WHO is giving the lecture?" but "WHAT is the lecture about?". The spirit of PMI's CCRS (Continuing Certification Requirements System) is such, that the content is important. Not the provider who delivers it. You will find the following statement in the PMP Credentials Handbook:
"PDU Activities for PMP credential holders must be related to project management topics that are substantially consistent with the knowledge areas and processes outlined in the current edition of the PMBOK Guide and involve appropriate expert resources."
So as long as the presentation, lecture, workshop, symposium or conference that you attended is consistent with this and the presentation is made by a "real expert", then you can claim your attendance as category 4 PDUs ("Other Providers").
There is just one caveat: You might get audited and have to prove validity of the presentation for your PDU claim.
My recommendation is therefore that it's always safer to participate in an event from a PMI Registered Education Provider because such events are pre-approved by PMI. If you attend a non PMI R.E.P. event, then keep as much documentation as you possibly can from the event. For instance I would keep: The agenda, a speaker bio, confirmation of attendance and (if possible) a copy of the presentation slides.