Inclusion Criteria:  Age ≥18 years of age at the time of signing the informed consent.  Histologically or cytologically confirmed metastatic NSCLC (squamous or nonsquamous) with no known actionable driver mutations (ex. EGFR, ROS1, ALK).  Patients must have had documented disease progression during or after 1 or 2 lines of systemic treatment for recurrent or metastatic disease. Two components of treatment must have been received in the same line or as separate lines of therapy: (i) a maximum of 1 line of platinum-containing chemotherapy regimen for recurrent/metastatic disease, and (ii) a maximum of 1 line of a locally approved/authorized PD-1/PD-L1 mAb containing regimen for recurrent/metastatic disease. Maintenance therapy following platinum doublet-based chemotherapy is not considered as a separate line of therapy. Maintenance therapy is defined as therapy given within 42 days after the last dose of platinum-based chemotherapy in patients with ongoing clinical benefit (complete response [CR], partial response [PR] or stable disease [SD]). Measurable or non-measurable disease per RECIST v1.1. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 2. A formalin-fixed paraffin-embedded (FFPE) tumor specimen (from archival or fresh biopsy) with an associated pathology report documenting NSCLC must be available to send to the Sponsor, within the specified timeframe, for planned retrospective biomarker analyses. Adequate organ function defined by the normal laboratory values.  Exclusion Criteria:  Prior therapy with docetaxel. Any contraindication to the administration of docetaxel at the discretion of the investigator. Mixed NSCLC/SCLC, or lung tumors whose predominant histology is sarcomatoid, or neuroendocrine. Any chemotherapy, immunotherapy, biologic, investigational, or hormonal therapy for cancer treatment (except for adjuvant hormonal therapy for breast cancer or prostate cancer defined as M0 disease or prostate-specific antigen (PSA) persistence/recurrence without metastatic disease) within 3 weeks prior to the first dose of trilaciclib/placebo. Any radiotherapy within 2 weeks prior to the first dose of trilaciclib/placebo. Presence of central nervous system (CNS) metastases requiring immediate treatment with radiation therapy or steroids (i.e., patient must be off steroids administered for brain metastases for at least 14 days prior to the first dose of trilaciclib/placebo). Presence of leptomeningeal disease. Significant third-space fluid retention (ex. ascites or pleural effusion) not amenable to required repeat drainage. QT corrected using Fridericia's formula (QTcF) interval >480 msec at screening (confirmed on repeat). For patients with ventricular pacemakers, QTcF >500 msec. Symptomatic peripheral neuropathy. History of interstitial lung disease (ILD). Prior allogeneic or autologous hematopoietic stem cell or bone marrow transplantation.