Fit curve in spaghetti plot

Question

For descriptive plots in R studio, I would like to fit a regression curve in my spaghetti plot. To create the spaghetti plot I used:

library(lattice)

GCIP <- data_head$GCIP
time_since_on <- data_head$time_since_on
Patient <- data_head$Patient
Eye <-data_head$Eye

xyplot(GCIP~time_since_on, groups = Patient, type='b', data=data_head)

and I've got this plot

Then I wanted to fit a polynomial curve, so I used this code:

plot.new<- plot(time_since_on,GCIP)
lines(lowess(GCIP ~ time_since_on))

This is what I've got:

What I want is to fit a curve like the one I've got in the image 2 but over the spaghetti plot (with the longitudinal data for each subject).

I've tried to use this code:

library(ggplot2)
library(reshape2)

GCIP <- data_head$GCIP
time_since_on <- data_head$time_since_on
Patient.ID <- data_head$Patient.ID
Eye <-data_head$Eye
Visit <-data_head$Visit
Patient<-data_head$Patient

ggplot(data = reprex, aes(x,y)) +
  geom_point(alpha=1, size=2) +
  aes(colour=Patient.ID) +
  geom_text(aes(label=label), size=2, colour='white') +
  geom_path(aes(group=Patient.ID))

ggplot(data= reprex, aes(x = time_since_on, y = GCIP)) + 
  geom_point(size = 2, alpha= 1,  aes(color = Patient.ID)) + #colour points by group
  geom_path(aes(group = Patient.ID)) + #spaghetti plot
  stat_smooth(method = "lm", formula = y ~ x, aes(group = Patient.ID, colour = group)) + #line of best fit by group
  ylab("GCIP (volume)") + xlab("time_since_on (months)") +
  theme_bw()

But I don't get anything from this.

COuld anyone help me please?

Here an example taken from the internet

Million Thanks.

Lili