Is the linear mixed-effects model the right choice for analysing my data? I'm in desperate need of advice in terms of the choice of statistical test for my analysis.
Briefly to explain what I am analyzing in an animal model:
I want to see the effect of 2 categorical variables ("genetic_profile" and "sex") and "age" variable (recorded in exact days which vary between subjects but the data is generally split into 3 and 9 months-old) on the continuous variable - "measurement". There are 52 measurements (24 come from paired animals - i.e. measure was taken twice in 12 out of 38 animals). The measurement was taken using a program that displays processed brain images and two points were selected manually to measure the thickness of a small anatomical feature.
Outcome variable: measurement
Predictor variables: genetic_profile (mutant/wild-type), sex (female/male), age (in days),
This is the model in R (also accounting for a possible interaction between genetic_profile and age). The random effect comes from animal.
model = lmer(measuremnet ~ Genetic_profile*Age + Gender + 
        (1 | animal), data = data_set)

I attached a picture of a plot of residals vs fitted (plot(model)) and it definitely does not look like the right fit (residuals form 3 parallel stripes across the plot).
I believe it's important to mention that measurement has presumably a large degree of error since the precision measure was to just 1 decimal place and essentially all measurements that were recorded were between 0.3 and 0.5 (differed by 0.1, 0.2 or 0.3 mm at most).
Should I try and find a way to apply this model or was the suggestion wrong? I presume that a t-test should be applied if the linear mixed model is incorrect?
 A: If I understand your description of your data, you have 52 observations (rows in your dataframe) and you try to fit a model with 7 parameters (intercept, variance of the random effect, general variance, 3 parameters for the interaction and one parameter for the age). As a rule of thumb, it is recommended to have between 20-30 observation per parameter. It is even more important when you expect to observe weak effect or a lot of variance in your outcome variable. I think that your biggest problem here is to fit a too much complicated model with not enough data.
A: Your measurement processes is incompatible with linear regression.  Given that your computer program rounds the measurement, and given the latent measurement is so low variance that it falls within 3 buckets, my recommendation is to reconsider the model likelihood and perform an ordinal logistic regression.
Jeremy raises a good point that you have a problem with your parameter budget.  52 observations (assuming the 1 in 10 rule for binary logistic regression, which has been shown to be very liberal and in fact any such rule would require many more observations per parameter) would allow you to adjust for 4 additional parameters.
You should strongly rethink rethink how to approach the model, starting with the likelihood.
