You technically need quite a bit of level-3 units if you're going to get unbiased parameter estimates in a 3-level model (generally speaking, sample size in any multilevel model is particularly important at the highest level), so unless you have a large random sample of countries (50+ perhaps), you should probably consider running separate 2-level models, or if you have few countries, you could consider treating country as a categorical level-2 predictor in a 2-level model –  Patrick Coulombe

Specifying a random effect involves assuming that the means of those levels are samples from a normal distribution. Better to specify them as fixed effects, AKA dummy variables if this assumption doesn't fit your data. In this way you are controlling for groupwise heterogeneity in the mean (at that level), but you are NOT allowing for heterogeneity in responses to your lower-level variables.

If you expect heterogeneity in response to your lower-level explanatory variables, separate models make sense, unless you want to run some sort of random coefficient model (which again involves the assumption that coefficients are normally distributed).

(I believe there are methods for non-normal random effects, but nothing as widely used or accessible as lme)