Seven years ago you presented yourself at Heathrow as a US citizen and requested visa-free entry. Visa-free entry requires that you don't work, and that you do not apply for public funds. It also assumes that you will leave the UK within a reasonable period of time.
When questioned you announced your intention to work, and to earn money for it. Since this breaches the terms under which you would be admitted, you were denied entry.
Now, you're proposing to arrive at Heathrow and request entry a second time. Immigration computers have long memories and the border guard will know about a prior refusal. You will be questioned, perhaps at length. If you try and lie your way through you'll be denied a second time and you can forget visiting the UK for a long time.
You need to persuade the border guards that you will comply with the terms of visa-free entry, and with your previous refusal you can expect them to be skeptical about any claims you make.
You should document links to the US, focussing on anything that requires your presence there, to show that you have reason to leave the UK. You should document your income and savings to show that you can afford your visit. And you need a convincing explanation for why things are different this time and you aren't going to work.
You could just show up at Heathrow with all this documentation and try to persuade the border guards to let you in. It can be done, but you could be detained for some hours.
Or, you can apply for a Visitor's visa before you leave the US. If you get the visa, great! If you don't, you avoid the questions and pain at Heathrow. And if the UK border guards ask why you have a visa, just explain about the prior refusal and that you wanted to be sure you'd be allowed to enter.
