First, since she's abandoned the apt, get a new roommie ASAP to help cover expenses. Second, sue R for her share of the rent & utilities. Small claims court is probably best. Then you'll have to garnish her wages, seize her car, etc. Third, turn her stuff over to L to sell. L has a landlord's lien on her stuff. If L takes physical possession of the stuff, L can hold the stuff hostage for 15-45 days, then sell the stuff to cover her bills. (L can even sell it to you if you like any of it.) Fourth, ask L to exercise his remedies under the abandonment clause of the lease (or under state law). L can declare she's abandoned the apt & you can require L to change the locks for security reasons. This also allows L to take her share of the security deposit to cover her check. (L has to send the statement of deductions within the state time limits.) Tell L that s/he has to cooperate with you or you can't cover the entire rent AND you'll argue that L shouldn't be able to collect full damages from you because L didn't mitigate his/her damages by seizing her stuff & letting you find a new roommie.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.