Because your model uses longitudinal data, it is best to check for the ICC before assuming independence. However, this particualr model has a small sample size, so it is singular,

    require(lme4)
    my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
    isSingular(my_lme)
    [1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

        require(blme)
        my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
                       formula=Size~Time+(Time|Group),data=my_data)
    isSingular(my_blmer)
    [1] FALSE
So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:
    

        summary(my_blmer)
    Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
    Prior dev  : -1.4809
    
    Linear mixed model fit by REML ['blmerMod']
    Formula: Size ~ Time + (Time | Group)
       Data: my_data
    
    REML criterion at convergence: -7.2
    
    Scaled residuals: 
         Min       1Q   Median       3Q      Max 
    -2.74016 -0.23951 -0.04383  0.26814  2.76185 
    
    Random effects:
     Groups   Name        Variance Std.Dev. Corr 
     Group    (Intercept) 0.54671  0.7394        
              Time        0.01784  0.1336   -0.98
     Residual             0.01331  0.1154        
    Number of obs: 20, groups:  Group, 3
    
    Fixed effects:
                Estimate Std. Error t value
    (Intercept)  0.25213    0.43100   0.585
    Time         0.06510    0.07882   0.826
    
    Correlation of Fixed Effects:
         (Intr)
    Time -0.970

The ICC is quite large: 0.546/(0.546+0.017+0.133)=0.78. Thus, you should be using an HLM. Also, because you have a small sample size, you should use a Bayesian HLM.