Estimating covariate-conditional treatment effects in multi-arm oncology studies is complicated when treatment arms have common distributional features and a non-negligible fraction of patients achieve long-term remission. We propose a joint mixture cure model with covariate-dependent mixtures of log-normal kernels with treatment-specific inclusions. Both linear and neural-network-assisted non-linear covariate links are proposed. Specifically, the susceptible survival distributions use a common finite dictionary of log-normal components, and then a binary inclusion matrix determines which components are active in each treatment arm. All parameters, including the hidden bases of the neural network, are learned jointly, while the output coefficients remain treatment- or component-specific. Posterior inference is performed using gradient-based MCMC, and treatment effects are summarized by covariate-conditional differences in restricted mean survival time (RMST). Variable importance is assessed using thresholded marginal best linear projections with data partitioning. Across two simulation settings, the proposed method demonstrates good finite-sample performance, with lower RMST-based estimation error than flexsurvcure. Compared with pairwise grf fits, the proposed method yields lower RMST-contrast MSE in most comparisons while ensuring mutually coherent multi-treatment contrasts. Finally, the application to the AALL0434 trial reveals covariate-dependent patterns in RMST posterior across methotrexate-based regimens and provides new insights into how these differences vary with patient covariates, highlighting the method's practical utility for studying heterogeneous treatment effects in pediatric oncology trials.

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