A Study of Trastuzumab Emtansine in Participants With Human Epidermal Growth Factor Receptor (HER)2 Immunohistochemistry (IHC)-Positive, Locally Advanced or Metastatic Non-Small Cell Lung Cancer (NSCLC)

Inclusion Criteria:

* Histologically or cytologically documented diagnosis of Stage IIIB not amenable to radical treatment or Stage IV NSCLC (pathological characterization must determine the non-squamous or squamous histological subtype as well as adenocarcinoma subtype classification)
* HER2 status of IHC 2+ or 3+ as determined by a Sponsor-designated central laboratory
* Prior treatment with at least one regimen of platinum-based (cisplatin or carboplatin) chemotherapy in the locally advanced or metastatic setting/recurrent NSCLC with documented disease progression by investigator assessment
* Participants with a known anaplastic lymphoma kinase (ALK) fusion oncogene (must be documented in the participant's chart) must have also experienced disease progression or intolerance with a first-line ALK Tyrosine Kinase Inhibitor (TKI) approved for the treatment of ALK fusion oncogene NSCLC (for example, crizotinib). Disease progression or intolerance must be documented
* Participants with a known mutation in the epidermal growth factor receptor (EGFR) gene (must be documented in the participant's chart) must have also experienced disease progression or intolerance with an EGFR TKI approved for the treatment of EGFR-mutant NSCLC (for example, gefitinib, erlotinib, afatinib). Disease progression or intolerance must be documented
* Measurable disease determined as per the RECIST v1.1
* Life expectancy of at least (\>/=) 12 weeks
* Adequate organ function
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Left ventricular ejection fraction (LVEF) \>/= 50 percent (%) by either echocardiogram (ECHO) or multiple-gated acquisition (MUGA) scan
* Use of highly effective contraception

Exclusion Criteria:

Cancer-Related Criteria:

* Any approved anti-cancer therapy less than or equal to (\</=) 21 days (including chemotherapy or hormonal therapy) before the first study treatment; the following exceptions are allowed: (1) TKIs approved for the treatment of NSCLC must be discontinued greater than (\>) 7 days prior to the first study treatment on D1C1 (The baseline computed tomography \[CT\] scan must be completed after discontinuation of TKIs); (2) Hormone-replacement therapy or oral contraceptives; (3) Anti-emetics, Granulocyte-colony stimulating factor (GCS-F), and prophylactic antibiotics according to local standards
* Investigational therapy participation in another clinical study with therapeutic intent \</= 21 days before first study treatment
* Previous irradiation is permitted if \>/=14 days since the last fraction of radiotherapy have elapsed before the first study treatment on Day 1 as long as a sufficient number of target lesions remain to allow for measurable disease as per RECIST v1.1
* Participants who have untreated brain metastases or are symptomatic; participants with treated brain metastases must have discontinued corticosteroid therapy and not have any neurological symptoms
* History of intolerance (including Grade 3 or 4 infusion reaction) or hypersensitivity to trastuzumab or murine proteins or any excipient of the product
* History of exposure to the following cumulative doses of anthracyclines: Doxorubicin or liposomal doxorubicin \> 500 milligram per meter-square (mg/m\^2); Epirubicin \> 900 mg/m\^2; Mitoxantrone \> 120 mg/m\^2. If another anthracycline, or more than one anthracycline, has been used, the cumulative dose must not exceed the equivalent of 500 mg/m\^2 doxorubicin
* Peripheral neuropathy of Grade \>/= 3 per the National Cancer Institute Common Toxicity Criteria for Adverse Events Version 4.0 (NCI CTCAE v. 4.0)
* History of other malignancy within the last 5 years, except for appropriately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, Stage I uterine cancer, or other cancers with a similar outcome as those mentioned above

Cardiopulmonary Function Criteria:

* Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures
* Severe dyspnea at rest due to complications of advanced malignancy or requiring current continuous oxygen therapy
* Clinical history of active hemoptysis
* Evidence of active pneumonitis during screening
* Current unstable ventricular arrhythmia requiring treatment
* History of symptomatic congestive heart failure (CHF) New York Heart Association (NYHA) classes II-IV
* History of myocardial infarction or unstable angina within 6 months of enrollment
* History of a decrease in LVEF to \<50%

General Criteria:

* Current severe, uncontrolled systemic disease (for example, clinically significant cardiovascular, pulmonary, or metabolic disease)
* Major surgical procedure or significant traumatic injury within 28 days before enrollment or anticipation of the need for major surgery during the course of study treatment
* Current pregnancy or lactation
* Current known active infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C virus (HCV)