LONE TREE — An In-N-Out Burger joint slated to pop up near Park Meadows Mall next year could attract more than 1,300 hungry carfuls of customers a day seeking the famous Double-Double at the iconic California eatery — and all that beef could generate monster-sized traffic jams for this fast-growing suburb. The Lone Tree City Council is scheduled to vote Tuesday night on whether to give the final OK to the fast-food chain, which plans to erect and open a 3,867-square-foot restaurant at 9171 Westview Road about a year from now. Such enormous volume is expected at the Lone Tree In-N-Out, especially during its first year of operation, that the company is building a 26-car-deep drive-thru lane to handle the masses — the second-largest drive-thru queue among the burger chain’s more than 350 stores in six states, according to city documents. There will also be 47 parking spaces for those who prefer to venture inside for their food. “We expect to have a lot of interest in this site and people using In-N-Out,” said Justin Schmitz, director of public works and mobility for Lone Tree.