No clinically relevant interaction has been observed when Kaletra was coadministered with omeprazole (40 mg once daily) No dose adjustment necessary.
Kaletra Summary of Product Characteristics, AbbVie Ltd, January 2021.

Drug interaction studies reveal no clinically significant interaction between Kaletra and omeprazole. Coadministration of omeprazole (40 mg once daily for 5 days) and Kaletra tablets (400/100 mg twice daily for 10 days) was studied in 12 HIV- subjects. Lopinavir Cmax, AUC and Cmin increased by 8%, 7% and 3%, respectively. Coadministration of the same dose of omeprazole with once daily Kaletra tablets (800/200 mg once daily for 10 days) to 12 HIV- subjects resulted in decreases in lopinavir Cmax, AUC and Cmin of 6%, 8% and 29%, respectively.
Kaletra Prescribing Information, AbbVie Ltd, October 2020.

Pharmacokinetics of LPV were determined after administration of LPV/RTV (400/100 mg twice daily) alone and in combination with omeprazole (40 mg once daily) to 15 HIV+ subjects. No statistically significant effect of omeprazole on LPV exposure was observed (Cmax 9234 vs 11274 ng/ml; Cmin 4473 vs 5111 ng/ml; AUC 89.1 vs 98.5 mg.h/L; alone vs +omeprazole). Ritonavir pharmacokinetics were also unchanged in the presence of omeprazole.
Acid reduction with a proton pump inhibitor does not affect pharmacokinetics of lopinavir or ritonavir in HIV-infected subjects in lopinavir/ritonavir-based therapy. Overton ET, et al. 8th International Workshop on Clinical Pharmacology of HIV Therapy, Budapest, April 2007, abstract 60.

The effect of omeprazole (40 mg once daily) or ranitidine (150 mg once daily) on the lopinavir/ritonavir tablet (400/100 mg twice daily or 800/200 once daily) was assessed in HIV+ subjects. Neither omeprazole or ranitidine significantly altered lopinavir or ritonavir exposure after coadministration.
Lack of effect of acid-reducing agents on the pharmacokinetics of lopinavir/ritonavir tablet. Klein et al. 13th Conference on Retroviruses and Opportunistic Infections, Denver, February, 2006, abstract 578.

The effects of gastric acid reducing agents (proton pump inhibitors, H2 receptor antagonists or antacids) on lopinavir concentrations were assessed on 5 occasions over a 48-week period in antiretroviral naïve patients receiving lopinavir/ritonavir (400/100 mg twice daily or 800/200 mg once daily). No significant differences in lopinavir concentrations at any week were observed between patients receiving twice daily lopinavir/ritonavir alone (n=45) or with an acid reducing agent (n=7). For patients receiving once daily lopinavir/ritonavir alone (n=86) or with an acid reducing agent (n=8), no significant difference were observed, with the exception of higher lopinavir concentrations at week 24 for patients on acid reducing agents. Similar trends were observed for ritonavir. Further formal investigations of the effect of potent acid reducing agents on lopinavir/ritonavir pharmacokinetics are warranted.
Lack of effect of gastric acid reducing agents on lopinavir/ritonavir plasma concentrations in HIV-infected patients. Bertz RJ, Chiu YL, Naylor C, et al. 7th International Congress on Drug Therapy in HIV Infection, Glasgow, November 2004, abstract P279.

The effect of lopinavir/ritonavir (400/100 mg twice daily) on the metabolism of omeprazole (40 mg single dose in combination with warfarin and vitamin K) was studied in 7 healthy volunteers. Coadministration resulted in an increase in CYP2C19, leading to increased metabolism of omeprazole; the ratio of omeprazole to 5-hydroxyomeprazole decreased from 1.45±0.97 to 0.46±0.25. Increased doses of drugs metabolised primarily by CYP2C19 may be necessary for optimal management when given concomitantly with lopinavir/ritonavir.
Lopinavir/ritonavir induces CYP2C9 and 2C19 activity as measured by warfarin and omeprazole biomarkers in healthy human volunteers. Yeh R, Gaver V, Park J, et al. 5th International Workshop on Clinical Pharmacology of HIV Therapy, Rome, April 2004, abstract 4.1.