I would like to share some of my thoughts when trying to improve the model fitting time of a linear mixed effects model in R using the lme4 package. <
If you use glmer rather than lmer, there is a parameter nAGQ. I found that setting nAGQ=0 dramatically reduced the time it took to fit a fairly complex model (13 fixed effects, one random effect with varying intercept and slope, 300k rows). This basically tells glmer to use a less exact form of parameter estimation for GLMMs. See ?glmer for more details, or this post.