Which model does the cv.glment uses to fit and why is it different? Using R

Question

I am working with R to build a predictive model using Binary Logistic with the Lasso penalty.

Originally that data set consisted of 63147 observations and 22 variables, with 3% of the observations coming from $G_1$ and 97% coming from $G_2$. As can be seen this is very unbalance so I have taken a sample of 30% coming from $G_1$ and 70% coming from $G_2$ with a sample size of 5000.

I have tried fitting 2 models, the classical binary logistic regression (BLR) using the glm package in R-software and the binary logistic regression with the Lasso penalty using glmnet package.

I have scaled my data using the scale function in R because the variables were measured using different measurements.

When fitting the BLR an error occurred as can be seen below:

> BLR.Model.SubPop <- train(y~., data = Train.Data.SubPop, method = "glm", family = "binomial")
There were 47 warnings (use warnings() to see them)
> warnings()
Warning messages:
1: glm.fit: algorithm did not converge
2: glm.fit: fitted probabilities numerically 0 or 1 occurred
3: glm.fit: algorithm did not converge
4: glm.fit: fitted probabilities numerically 0 or 1 occurred
5: glm.fit: algorithm did not converge
6: glm.fit: fitted probabilities numerically 0 or 1 occurred
7: glm.fit: algorithm did not converge)

From the research I have done this is due to separation in our data.

I had then opted to used BLR with the LASSO where I have used the cv.glmnet() function to find lamnda.min and lambda.1se

Below are the coefficients for the above mentioned values of lambda

> cv.lasso <- cv.glmnet(x, y, alpha = 1, family = "binomial", type.measure = "class")
> plot(cv.lasso)
> cv.lasso$lambda.min
[1] 5.575006e-05
> cv.lasso$lambda.1se
[1] 0.0001173485
> coef(cv.lasso,cv.lasso$lambda.min)[,1]
                (Intercept) X1     X2             X3       
-94.7714913 0   0.17288133  -0.28371818 0.03050103
     X4         X5  X6      X7         X8   X9
0.02482283  0   0   -0.26218308 0
X10 X11         X12 X13 X14
0   -2.00853016 0   0   0
X15          X16           X17  X18 X19
-0.01768456 0.56538543  0   0   0.54166489
X20             X21         
30.10519005 0.18198277

(Intercept) X1  X2            X3            X4
-71.93503132    0   0.0644656   -0.287559336    0.001068958
X5         X6   X7  X8  X9
0.017905135 0   0   0   0
X10 X11        X12  X13 X14
0   -1.239442745    0   0   0
X15        X16  X17 X18 X19
-0.083885831    0   0   0   0.19158206
X20         X21         
22.99517148 0.052543166         

When I tried to fit the Lasso using lambda.min and lambda.1se I encountered the below warning.

> lasso.model.1se <- glmnet(x, y, alpha = 1, family = "binomial", lambda = cv.lasso$lambda.1se)
Warning messages:
1: from glmnet Fortran code (error code -1); Convergence for 1th lambda value not reached after maxit=100000 iterations; solutions for larger lambdas returned 
2: In getcoef(fit, nvars, nx, vnames) :
  an empty model has been returned; probably a convergence issue

However, when I run the below code it run

LASSO.prob <- cv.lasso %>% predict(newx=x.test,type = "response")

I am not sure which lambda cv.lasso is working with, is it lambda.min or lamnda.1se? Why am I getting the errors?

I used the below link as a reference to build my code:

http://www.sthda.com/english/articles/36-classification-methods-essentials/149-penalized-logistic-regression-essentials-in-r-ridge-lasso-and-elastic-net/?fbclid=IwAR0ZTjoGqRgH5vNum9CloeGVaHdwlqDHwDdoGKJXwncOgIT98qUXGcnV70k