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A few comments on this matter:

• I don't think reducing equity is the solution you want.  This would essentially be the equivalent of a sale of the one member's equity. 
  • Here you would need to determine the value of the units each year and compare that to the rent paid to determine the reduction in equity.
  • As a result of this, you would not receive any tax deduction as this is a redemption of the one member's interest every year.
  • This member would then need to report a gain or loss every year; if a gain, tax with no cash...not a good result.
  • I'm not sure this is the result the one member is looking for
• I also agree that paying the rent for the one member wouldn't pass the test for a tax deduction at the LLC level; in general, see next bullet.  
• The only way to receive a tax deduction is to treat the rent paid as a guaranteed payment to the one member.  A guaranteed payment is an amount paid to a partner (member) without regard to the income of the LLC.  In essence, that is exactly what is happening.
  • This is then specifically allocated to that member on the K-1 and will be picked up as SE income on the member's personal tax return.
• You need to have a consultation with the member's and a tax professional where you can discuss the goals of the LLC and the investing member.
• You don't mention if the other two LLC member's made any equity contribution.
  • Are they receiving a profits interest?
  • Does the current formation and equity make economic sense?
  • Will this LLC be profitable from day 1 (year 1)?
    • This is a big deal based on the current limited facts.
    • You may generate a loss with two profits interest member's who will not receive any allocation and the entire loss be allocated to the LLC member who contributed the equity but is not active, hence the losses will be passive and possibly of no current use (no current income tax benefit).
• You definitely need to make sure you understand the logistics of how the economics of this LLC will flow and the impact to the respective member.  Spend the $$ to make sure you understand how this works now and not later.  This investment in tax advice will pay off.