How to combine result of lapply to a data.frame?

You can also use data.table's rbindlist as follows:

require(data.table)
df <- setDF(rbindlist(lapply(my_vector, my_function)))

Without setDF rbindlist returns a data.table instead of a data.frame

Try

library(dplyr)
lapply(my_vector, my_function) %>% bind_rows()