Lymphogranuloma venereum is treated with antibiotics. The first choice of treatment is doxycycline, but macrolides (erythromycin) and sulfa drugs (sulfamethoxazole/trimethoprim) have also been shown to be effective. Azithromycin, ofloxacin, and levofloxacin are also recommended as treatments for chlamydial diseases.
As with the more common forms of chlamydia, your partner should also be treated if you have been diagnosed with and treated for Lymphogranuloma venereum.
Sources:
McLean CA, Stoner BP, Workowski KA. "Treatment of lymphogranuloma venereum." Clin Infect Dis. 2007 Apr 1;44 Suppl 3:S147-52.
Van Vranken M. "Prevention and Treatment of Sexually Transmitted Diseases: An Update" Am Fam Physician 2007;76:1827-32. (Accessed online 3-18-08)

