China

China doesn't lend us anything. China sells us goods. We give them US dollars. Those US dollars are parked in China's savings account at the Fed. China wants to make some interest on those dollars rather than have them sit there (since China isn't buying much back from the US with those dollars). So China buys govt' paper and the Fed moves the dollars from China's savings account to China's checking account at the Fed. There's your debt. Note it had nothing to do with deficits. When China's "debt" comes due, the Feds move the dollars out of China's checking account and back into their savings accounts with the interest added. All of this is done by a computer marking up the accounts at the Fed. Your tax dollars never pay for it. Welcome to the modern monetary system.

I think you have conflated the trade deficit and the budget deficit somewhat. Each influences the other but they also function separately. The trade deficit is caused by US consumers overspending on imports, the government budget deficit is caused by the government borrowing to cover operating costs that exceed tax revenue.

Chinese demand for US Treasury debt is fueled by their trade surplus with the US, like you wrote, but not all the excess dollars they accumulate return to purchase notes and bonds. Many of those dollars are converted into other currencies by China, or into precious metals, or into the bonds of other governments, or into commodities.