The field of lung nodule detection and cancer prediction has been rapidly developing with the support of large public data archives. Previous studies have largely focused cross-sectional (single) CT data. Herein, we consider longitudinal data. The Long Short-Term Memory (LSTM) model addresses learning with regularly spaced time points (i.e., equal temporal intervals). However, clinical imaging follows patient needs with often heterogeneous, irregular acquisitions. To model both regular and irregular longitudinal samples, we generalize the LSTM model with the Distanced LSTM (DLSTM) for temporally varied acquisitions. The DLSTM includes a Temporal Emphasis Model (TEM) that enables learning across regularly and irregularly sampled intervals. Briefly, (1) the temporal intervals between longitudinal scans are modeled explicitly, (2) temporally adjustable forget and input gates are introduced for irregular temporal sampling; and (3) the latest longitudinal scan has an additional emphasis term. We evaluate the DLSTM framework in three datasets including simulated data, 1794 National Lung Screening Trial (NLST) scans, and 1420 clinically acquired data with heterogeneous and irregular temporal accession. The experiments on the first two datasets demonstrate that our method achieves competitive performance on both simulated and regularly sampled datasets (e.g. improve LSTM from 0.6785 to 0.7085 on F1 score in NLST). In external validation of clinically and irregularly acquired data, the benchmarks achieved 0.8350 (CNN feature) and 0.8380 (LSTM) on area under the ROC curve (AUC) score, while the proposed DLSTM achieves 0.8905.