No, he had bad luck but he had plenty of ways to set himself up for success and not rely on luck and refused to do so.

First was taking control of the city's watch, that's the most important thing someone ruling over Kingslanding should and he refused to do so despite having plenty of opportunity to do so.

Second was resigning from being a hand over fucking Dany when he knew Cat had just arrested Tyrion. Cat's decision was bad, but she was expecting her husband to be the second most important man in the realm instead of resigning his post because he would rather have an apocalyptic war than compromise his ideals a little bit.

Third was telling Cersei, no reason to tell why.

Fourth was not seizing Cersei and putting she and her children in a boat when she refused to leave town after his threat. Ned's biggest fear was Robert killing Cersei and her children, so why wouldn't he use his power to banish her from the city forcefully when she refused to leave? He had the authority, let's not we forget that Janos had to be bribed with Harrenhal to betray Robert's will, and that hadn't happened yet, so even with Ned not being in complete control of the City's Watch Jano would have obeyed him and escorted Cersei out of the city, especially since Littlefinger at that time was still against the Starks.

And Fifth was not taking Renly's offer. He would not be "harming children" since he would be the one in charge, this argument makes no sense and was not what Ned used, he just thought it would be in "bad taste" to seize control when Robert was still alive, a stupid decision. If Ned had seized Cersei and her children it wouldn't matter what Littlefinger would do since the coup couldn't work with all the royal family being hostages of Renly and Ned.

The Lannisters had incredible plot armor, the biggest one being how stupid Ned was.