It would be hard to get it from lm and aov.  You would have to be better than most of us at calculating the expected mean squares for your design to be able to estimate the variances that you need to calculate heritability.

Use lme or asreml-r to estimate the genetic variance and interactions as random effects and extract the error variance.

Dear Ahmad 

what i have done to calculate heritablity in a factorial design with three factors ( A,B, C ) and replication (R) are shown below.

when all three factors are Random

H2 for factor A =((MS_a - MS_ab - MS_ac + MS_abc) /rbc) / (MS_a / rbc)     when all three factors are Random

H2 for factor B =((MS_b - MS_ab - MS_bc + MS_abc) /rac) / (MS_b / rac) when all three factors are Random

H2 for factorC =((MS_c - MS_ac - MS_bc + MS_abc) /rab) / (MS_c / rab) when all three factors are Random

Now lets assume these three factors are fixed

H2 for factor A =((MS_a - MS_error) /rbc) / (MS_a / rbc)

H2 for factor B =((MS_b - MS_error) /rac) / (MS_b / rac)

H2 for factor C =((MS_c - MS_error) /rab) / (MS_c / rab)

i go further with a little more  complexity,  when  A and B are random and C is fix

H2 for factor A =((MS_a - MS_ac) /rbc) / (MS_a / rbc)

H2 for factor B=((MS_b - MS_bc) /rac) / (MS_b / rac) 

H2 for factor C =((MS_c - MS_error) /rab) / (MS_c / rab)

a=levels for Factor  A

b=levels for Factor  B

c=levels for Factor  C

MS=Mean of Square which is shown in all ANOVA tables.

just  manually replace  data in the given commends and run them in R.

hope it would be useful 

Hi Mohammed, I was so lazy to calculate this because I do have much time. But it seems that I should do this....