Correct me if I am wrong, but I think based on the output table the model needs to be specified as follows in order to make sure the fixed effect is called as a fixed effect and not a random effect.

lmer(Biomass_kg_sqrt~Protection + (1|Protection:Site.Name),fish)
Linear mixed model fit by REML 
Formula: Biomass_kg_sqrt ~ Protection + (1 | Protection:Site.Name) 
   Data: fish 
   AIC   BIC logLik deviance REMLdev
 180.5 194.8 -85.26    160.6   170.5
Random effects:
 Groups               Name        Variance   Std.Dev.  
 Protection:Site.Name (Intercept) 7.3865e-12 2.7178e-06
 Residual                         2.1026e-01 4.5854e-01
Number of obs: 128, groups: Protection:Site.Name, 19

Fixed effects:
                       Estimate Std. Error t value
(Intercept)            1.431102   0.051590  27.740
Protection[T.MPA_GUA]  0.004107   0.117166   0.035
Protection[T.NTZ_FPR] -0.223089   0.098337  -2.269

Correlation of Fixed Effects:
            (Intr) P[T.MP
P[T.MPA_GUA -0.440       
P[T.NTZ_FPR -0.525  0.231