Ahmet, thanks for reporting this and providing a fix! I'm pretty sure this was caused by
SOLR-2382, see item #6 in the description "change the semantics of entity.destroy()". And I do think your fix is correct: just close the reader when it runs out of data so that the next time around it will open a new reader on the next file in the list. LEP is the only EntityProcessor that depended on the old semantics of destroy().
The disturbing thing here is that TestLineEntityProcessor passes, so clearly it is not testing the combination of FLEP/LEP correctly, even though the code comments indicate this was the intention. Likely we need to replace this test with something in the spirit of the test included with
SOLR-3307, or at least improve the mock-up LEP with something more realistic. In any case, we'll need a unit test that actually fails prior to your patch and then passes with it applied...