Longitudinal brain MRI is essential for characterizing the progression of neurological diseases such as Alzheimer's disease assessment. However, current deep-learning tools fragment this process: classifiers reduce a scan to a label, volumetric pipelines produce uninterpreted measurements, and vision-language models (VLMs) may generate fluent but potentially hallucinated conclusions. We present LoV3D, a pipeline for training 3D vision-language models, which reads longitudinal T1-weighted brain MRI, produces a region-level anatomical assessment, conducts longitudinal comparison with the prior scan, and finally outputs a three-class diagnosis (Cognitively Normal, Mild Cognitive Impairment, or Dementia) along with a synthesized diagnostic summary. The stepped pipeline grounds the final diagnosis by enforcing label consistency, longitudinal coherence, and biological plausibility, thereby reducing the risks of hallucinations. The training process introduces a clinically-weighted Verifier that scores candidate outputs automatically against normative references derived from standardized volume metrics, driving Direct Preference Optimization without a single human annotation. On a subject-level held-out ADNI test set (479 scans, 258 subjects), LoV3D achieves 93.7% three-class diagnostic accuracy (+34.8% over the no-grounding baseline), 97.2% on two-class diagnosis accuracy (+4% over the SOTA) and 82.6% region-level anatomical classification accuracy (+33.1% over VLM baselines). Zero-shot transfer yields 95.4% on MIRIAD (100% Dementia recall) and 82.9% three-class accuracy on AIBL, confirming high generalizability across sites, scanners, and populations. Code is available at https://github.com/Anonymous-TEVC/LoV-3D.