Inclusion Criteria:

* Is the age of majority in their country
* Has pathologically documented breast cancer that:

1. is unresectable or metastatic
2. has confirmed HER2-positive expression as determined according to American Society of Clinical Oncology - College of American Pathologists guidelines evaluated at a central laboratory
3. was previously treated with ado-trastuzumab emtansine (T-DM1)
* Has documented radiologic progression (during or after most recent treatment or within 6 months after completing adjuvant therapy)
* Is HER2 positive as confirmed by central laboratory assessment of most recent tumor tissue sample available. If archived tissue is not available, agrees to provide a fresh biopsy.
* Male and female participants of reproductive/childbearing potential must agree to use a highly effective form of contraception or avoid intercourse during and upon completion of the study and for at least:

1. 7 months after the last dose of DS-8201a (females); 4.5 months after last dose of DS-8201a (males)
2. 6 months after the last dose of lapatinib/capecitabine for female participants (3 months for male participants)
3. 7 months after the last dose of trastuzumab/capecitabine
* Has adequate hematopoietic, renal and hepatic functions

Exclusion Criteria:

* Has previously participated in an antibody drug conjugate study sponsored by Daiichi Sankyo. Prior treatment in the adjuvant/neo-adjuvant setting would be allowed if progression of disease did not occur within 12 months of end of adjuvant therapy
* Has had prior treatment with capecitabine
* Has uncontrolled or significant cardiovascular disease
* Has a history of (noninfectious) interstitial lung disease (ILD)/pneumonitis that required steroids, has current ILD/pneumonitis, or suspected ILD/pneumonitis that cannot be ruled out by imaging at screening
* Has active central nervous system (CNS) metastases