You do not need to use LPs to build work stations. You use the coins you earn to increase your resource storage and you can trade resources to get the ones you need to build the work stations. Yes it takes a long time, but this game is not meant to be fast.
And if you want to earn LPs then have as many of your sims doing the cooking hobby as you can, when they're not working. I have ten of mine doing the hobby making the 5 or 20min meal and can usually earn about 10 LPs a day. I also have three toddlers doing the playhouse hobby and four sims doing the diving hobby. All hobbies earn LPs once you have completed them the first time.
