Existence of polynomial time reduction from P to R?

Question

Why the next idea doesn't work:

If L_2 in R and L_1 in P and the languages are not trivial, 
then there is a polynomial-time reduction from L_1 to L_2

I know that if such reduction exists, than L_1 is also in R --> But L_1 is in P and P is in R, so everything looks OK :)

Will be glad for your help here.