Is there a compendium of well-known (and elementary) Fibonacci/Lucas Number congruences? I've proven the following and would like to know if it is (a) trivial, (b) well-known, or (c) possibly new. $$ L_{2n+1} \pm 5(F_{n+2} + 1) \equiv (-1)^{n} \mod 10. $$ Is there a simple proof of this identity, requiring only basic identities of the two sequences? Any help or hints to this effect are certainly appreciated!

More generally, for integers $l,m,n$, we have $$ L_{12l + m+n} \pm 5(F_{60l + m} + F_{60l+ n} + F_{60l+ \text{gcd}(m,n)}) \equiv (-1)^{n} L_{12l + m - n} \mod 10. $$