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I'm trying to build a consolidated LOB from several direct feeds.

However, there are many instances in which for a given stock, the bid price in one venue equals or crosses the ask price in a different venue.

Is that a valid state or do I have an issue with out-of-order event processing across the different feeds? In such case, what's the best way to "fix" the LOB back to a valid state (e.g. ignore the locking/crossing event, remove the locked/crossed prices)?

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It is possible to observe it due to the latency between different exchange locations. You may try to fall back on SIP if it persists for more than a few seconds, though probably that part should be outside of your LOB construction.

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Generally you want to rebuild the book venue by venue. NBBO is a different story.

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