The question you have to ask yourself, is what are you trying to determine?  Or, more technically, what hypothesis are you trying to test?

Am I correct in understanding that you have 20 experimental units, and no treatments other than sampling over time?  In that case, what is it you want to know?

If you are wondering if there are changes in lipid percent over time, it sounds like your answer is already, “obviously yes”.

In this situation, it would be possible to do a nonlinear regression, with simply a y (lipid percent) and an x (days after first sample).  One issue with this is that your data points aren’t really independent (because they are from the sample individuals sampled over time).  A second issue is that if the data are heteroscedastic across months, you may have problems meeting the assumptions of this kind of model.  But this allows you to pick an appropriate theoretical model to explain the changes in lipid percent.  If so, I recommend using a p-value for the model, and some kind of pseudo-r-squared or other measure of goodness-of-fit.  You may have to transform your dependent variable.

A better approach would be to model the data as a mixed model which can take into account the repeated measures aspect.  Using month as a factor variable might work.  Or if you could treat time as a continuous variable, and you’d probably have to add in days-squared and days-to-the-third to account for the non-linearity over time.  This kind of modeling allows you to kind of normalize (in the colloquial sense of the word) the lipid values for each experimental unit.

But overall, it might just be best to plot the median or mean of each sampling date, and a confidence interval about this statistic.  Doesn’t this tell you everything you want to know?  It shows the changes in lipid percent over time.  It goes up after spawning and then drops down.  Medians with non-overlapping 95% confidence intervals are probably statistically significantly different.  If the lipid values are really variable across experimental units, you might have to normalize (in the colloquial sense of the word) the lipid values for each experimental unit.  Like, lipids as percent of initial value, or change in lipid percent value since initial measurement.

If you wanna go Bayesian you can use an hierarchical Bayesian model considering mixed effects

https://books.google.pt/books?id=iWg3z0bEdSQC&printsec=frontcover&dq=bayesian+hierarchical+models&hl=en&sa=X&redir_esc=y#v=onepage&q=bayesian%20hierarchical%20models&f=false

These kind of models behave pretty fine with missing data. For instance, if you haven't other variables besides time, you can consider a transformation of the response as Jochen Wilhelm said, e.g. logit. In this case you can consider that y represents the transfomed data and $y \sim N( m(t), \sigma )$, with $m(t) = \beta_0 + \beta_1 \times t + b_0 + b_1\times t$ being \bf{b}=(b_0,b_1)\sim N(0,\Sigma) a vector of random effectas and the relation is linear. But if you suspect that the relation is not linear you can add t^2 and t^3 and the respective random effects. From my point of view this is the simple strategy. For a complex one you can think about splines.

https://books.google.pt/books?id=iWg3z0bEdSQC&printsec=frontcover&dq=bayesian+hierarchical+models&hl=en&sa=X&redir_esc=y#v=onepage&q=bayesian%20hierarchical%20models&f=false

Thank you to all replies. I know the lipid seems obvious but I have also done fatty acids and they are not so obvious.

I am currently using a glm (in R), trialling different family distributions, however none fit very well. With each family there are options of using a different link and one is 'logit'. Is this what you mean by a logit transformation? Or would it be more like a log transformation, in that I am transforming the data before running the model?

I will look into Bayesian modelling.  Thank you very much.