Adding my strategy for this...
My sim began the challenge working her way through the empty lots. On each lot she adds three unique lot traits to each. She is able to complete the progression through the empty lots before running out of money.
After finishing up the empty lots, she moves into her first empty house. She gets the last three traits here. She is not going to move into any apartments so she won’t be able to get those locked lot traits for her count. Her final lot trait count is 36 traits.
She can’t afford the next move on her own so she moves in with Johnny Zest. From here she moves into occupied households in order to increase her funds and into empty houses when she can afford it. She did not do anything to earn money and did not leave anything on the lots when she moved out.
She completed several lot challenges on the way but avoided most of them during the moving process. Wild Foxes, Off-the-Grid, Simple Living, Filthy, and Reduce and Recycle are the challenges she completes as she moves.
She ends her moving when she joins Judith Ward in the most expensive house in the game. She turns on all of the remaining lot challenges and is able to finish everything except for Cursed. She completed 8 challenges - so not quite everything possible, but everything I had on my list to do.
Over the course of the challenge she lived on 55 different lots, used 36 lot traits, and completed 8 lot challenges.