Oil Separator Replaced. Check Engine Back On

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The check engine light was on about a month ago. I had the code checked and was told the engine was running lean. We weren't too concerned; tried to take it on a 3 hour drive and it just was SPEWING white smoke. We had it towed to a shop thinking head gasket - was oil separator. The check engine light is back on 3 weeks later. 54,000 miles. I am not the original owner. I am not technical. Doubt I could change a tire. What else could be wrong with this engine?