Assessing whether sigma for a random effects parameter is equal to 0

LRT = 8.1423, p-value = 0.0014
Is this result implying that the standard deviation for the random effect is significant such that we reject 
the null hypothesis and that H0: sigma = 0 is false?

Yes. And crosscheck 

 anova(lm(diameter ~ sample + factor(sample), data=pistonrings))
Analysis of Variance Table

Response: diameter
                            Df    Sum Sq    Mean Sq F value    Pr(>F)    
sample                 1 0.0022175 0.00221755 22.2785 5.115e-06 ***
factor(sample)  38 0.0077962 0.00020516  2.0612  0.001039 ** 
Residuals         160 0.0159260 0.00009954                      
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1