Rhodes struck his first red-ball century of the summer, an unbeaten 151, while Yates added the fifth of his prolific season as the Bears finished the second day at 464 for seven.
That represented a substantial lead of 386 runs to leave Warwickshire firmly on track to claim a second trophy inside a week.
Dominic Sibley and Sam Hain added half-centuries while Lancashire leg-spinner Matt Parkinson was rewarded for his toil on a placid pitch with three wickets.
Warwickshire captain Will Rhodes said: “It’s been unbelievable. If you could write two days of a script and how you want them to go that would be pretty close to it. We’re best part of 400 runs ahead, three days to go so I’m a very happy captain.”
Of the batting performance he added: “It was very strong. It was quite well documented we didn’t get 400 throughout the season and we came here to Lord’s and wanted to put that right and put on a show. There’s no better place than here.”
And reflecting on his own 100, he said: “It’s always nice to come here and score runs. I said before that the game that I hadn’t got a hundred all year and I wanted to finish the season strong. I feel like I’m hitting the ball really nicely so it’s nice to tick that one off. It’s a shame it’s not four months ago and I could carry a bit of form into the summer but it’s the right place at the right time.”
Rhodes lifted the LV= Insurance County Championship trophy on Friday with only a century missing from his honours list for the season.
The 26-year-old set about rectifying that in dominant style after he walked into bat alongside Yates in the morning session after Sibley was trapped lbe by Tom Bailey.
Lancashire had needed more early wickets to have any hope of recovering an already desperate situation after they were skittled for 78 yesterday, but Rhodes and Yates ensured such thoughts were quickly off the table.
The pair settled into a 110-run second-wicket stand that not only squeezed any life out of the Red Rose challenge but also underlined why Yates is being touted for higher honours.
The 22-year-old reached his century with the calm assurance that successful teams require at the top of the order.
When he finally departed, well caught by Luke Wells at slip off Parkinson, Rhodes simply kept gong to bat through the day and further reinforce his side’s position.
Rhodes struck 18 boundaries and shared a further 97-run stand with Hain, who was bowled Jack Blatherwick for 55.
Wells then bowled Matthew Lamb without scoring but Michael Burgess joined in the free scoring with 44 before Parkinson had him stumped.
Tim Bresnan and Danny Briggs both fell cheaply to the leg-spinners but Rhodes continued until the close to leave him and his side on the brink of a memorable week.