Prompted by your answer to Royce-Stark question, since Ned & Yohn were close acquaintances & distant kinsmen, why didn’t Ned ever consider enlisting Yohn & his personal guard’s support for his attempt to seize control in KL ? If a minor noble like Ser Lothor Mallory had 20 men with him in the capitol, surely Yohn would have at least that many swords ?

He did:

“I called you here to ask for the help you promised Catelyn. This is a perilous hour for all of us. Robert has named me Protector, true enough, but in the eyes of the world, Joffrey is still his son and heir. The queen has a dozen knights and a hundred men-at-arms who will do whatever she commands … enough to overwhelm what remains of my own household guard. And for all I know, her brother Jaime may be riding for King’s Landing even as we speak, with a Lannister host at his back.“
"And you without an army.” Littlefinger toyed with the dagger on the table, turning it slowly with a finger. “There is small love lost between Lord Renly and the Lannisters. Bronze Yohn Royce, Ser Balon Swann, Ser Loras, Lady Tanda, the Redwyne twins … each of them has a retinue of knights and sworn swords here at court.”
“Renly has thirty men in his personal guard, the rest even fewer. It is not enough, even if I could be certain that all of them will choose to give me their allegiance. I must have the gold cloaks. The City Watch is two thousand strong, sworn to defend the castle, the city, and the king’s peace.”

Ned thought they wouldn’t be enough.