Clinical studies have shown that there are no clinically significant interactions between abacavir, zidovudine, and lamivudine.
Ziagen Summary of Product Characteristics, ViiV Healthcare UK Ltd, October 2011.

Fifteen HIV-infected patients were enrolled in a crossover-designed drug interaction trial evaluating single doses of abacavir (600 mg), lamivudine (150 mg), and zidovudine (300 mg) alone or in combination. Analysis showed no clinically relevant changes in the pharmacokinetics of abacavir with the addition of lamivudine or zidovudine or the combination of lamivudine and zidovudine. Lamivudine exposure (AUC decreased 15%) and zidovudine exposure (AUC increased 10%) did not show clinically relevant changes with concurrent abacavir.
Ziagen Prescribing Information, ViiV Healthcare, June 2019.

Multiple dose pharmacokinetics were determined in HIV-infected subjects following coadministration of abacavir (200, 400 or 600 mg three times daily or 300 mg twice daily) alone or with zidovudine (200 mg three times daily or 300 mg twice daily). Coadministration of zidovudine had only small and inconsistent effects on the steady state pharmacokinetics of abacavir that did not increase with dose. At the clinical abacavir dose (300 mg twice daily), zidovudine coadministration had no effect on abacavir AUC. The pharmacokinetic profiles of zidovudine in the absence of abacavir were not determined; however, mean AUC and Cmax values for zidovudine in the presence of abacavir were comparable to historical steady state values.
Multiple-dose pharmacokinetics and pharmacodynamics of abacavir alone and in combination with zidovudine in human immunodeficiency virus-infected adults. McDowell JA, et al. Antimicrob Agents Chemother, 2000, 44:2061-2067.

The pharmacokinetics and safety of single doses of abacavir (600 mg), zidovudine (300 mg) and lamivudine (150 mg) were evaluated when given alone or with either or both of the other drugs to 13 HIV-infected subjects. Coadministration of abacavir with zidovudine (with or without lamivudine) decreased ZDV Cmax by ~20%, delayed ZDV Tmax by 0.5h and increased AUC of zidovudine glucuronide by up to 40%. There were no differences in the pharmacokinetics of abacavir when given alone, or with zidovudine or lamivudine, or with both zidovudine and lamivudine.
Single dose pharmacokinetics and safety of abacavir (1592U98), zidovudine, and lamivudine administered alone and in combination in adults with human immunodeficiency virus infection. Wang LH, et al. Antimicrob Agents Chemother, 1999, 43: 1708-1715.