The tricky part here is you cannot take a home office deduction on Schedule C unless you have sufficient income to offset the home office expenses. Because your income is reported on a K-1, Schedule C is not used.
The subject is discussed in IRS Publication 587.
"Partners You may be allowed to deduct unreimbursed ordinary and necessary expenses you paid on behalf of the partnership (including qualified expenses for the business use of your home) if you were required to pay these expenses under the partnership agreement."
https://www.irs.gov/publications/p587/ar02.html#en_US_2014_publink1000226431Enter your partnership K-1 information in TurboTax. Go through the screens, entering your information, and you will come to a screen entitled " Describe the Partnership". Check the box "I am required to pay supplemental business expenses...." See screenshot below. It is not as clean an entry as using the home office deduction interview, but you can enter the expenses necessary to include your home office deduction.
There have been several discussion threads in Turbo Tax, but none has reached a perfect solution. One thing to keep in mind is the LLC is treated as a partnership for tax purposes and Publication 587 does specify that the supplemental business expenses are spelled out in the partnership agreement.