complex mutation based on difference between two dates in two different data frames

A lubridate duration with some filtering of the visit data frame should do the trick:

library(dplyr)
library(lubridate)

User_ID <- c("1", "2", "3", "4","2", "5", "6","1", "4", "1")
User_disease <- c("a", "b", "c", "a" , "c", "d", "a", "s", "n", "b")
Diagnosis_date <- c("2020-11-23", "2020-10-12", "2020-11-25", "2020-09-30", "2020-12-23", "2020-12-12", "2020-10-28", "2020-12-09", "2020-06-24", "2020-08-15")
df1 <- data.frame(User_ID, User_disease, Diagnosis_date) %>%
  mutate(Diagnosis_date = ymd(Diagnosis_date))

User_ID_Visit <- c("1", "2", "3", "4","2", "5", "6","1", "4", "1", "1", "3", "3", "5", "6", "2", "1", "4", "3", "5")
Visit_date <- c("2020-09-23", "2020-09-12", "2020-11-14", "2020-09-23", "2020-12-12", "2020-12-10", "2020-09-24", "2020-12-07", "2020-06-13", "2020-08-12","2020-06-23", "2020-07-11", "2020-12-25", "2020-05-30", "2020-11-29", "2020-12-10", "2020-10-25", "2020-12-21", "2020-09-24", "2020-11-15")
df2 <- data.frame(User_ID_Visit, Visit_date) %>%
  mutate(Visit_date = ymd(Visit_date))

df1 %>%
  rowwise() %>%
  mutate(visited_last_month = any(between(filter(df2, User_ID_Visit == User_ID)$Visit_date %--% Diagnosis_date / ddays(1), 0, 30))) %>%
  ungroup()

# # A tibble: 10 × 4
#    User_ID User_disease Diagnosis_date visited_last_month
#    <chr>   <chr>        <date>         <lgl>             
#  1 1       a            2020-11-23     TRUE              
#  2 2       b            2020-10-12     TRUE              
#  3 3       c            2020-11-25     TRUE              
#  4 4       a            2020-09-30     TRUE              
#  5 2       c            2020-12-23     TRUE              
#  6 5       d            2020-12-12     TRUE              
#  7 6       a            2020-10-28     FALSE             
#  8 1       s            2020-12-09     TRUE              
#  9 4       n            2020-06-24     TRUE              
# 10 1       b            2020-08-15     TRUE  

Please notice that I made some changes to you input data.

I found a solution to my question. First I added an event ID column to df1. Then used inner join to create a new data frame df3 before I created a lubridate time interval to check whether a patient visited the hospital within 30 days prior to diagnosis.

library(dplyr)
library(lubridate)

User_ID <- c("1", "2", "3", "4","2", "5", "6","1", "4", "1")
User_disease <- c("a", "b", "c", "a" , "c", "d", "a", "s", "n", "b")
Event_ID <- 1:10
Diagnosis_date <- c("2020-11-23", "2020-10-12", "2020-11-25", "2020-09-30", "2020-12-23", "2020-12-12", "2020-10-28", "2020-12-09", "2020-06-24", "2020-08-15")
df1 <- data.frame(User_ID, User_disease, Event_ID, Diagnosis_date) %>%
  mutate(Diagnosis_date = ymd(Diagnosis_date))

User_ID <- c("1", "2", "3", "4","2", "5", "6","1", "4", "1", "1", "3", "3", "5", "6", "2", "1", "4", "3", "5")
Visit_date <- c("2020-09-23", "2020-09-12", "2020-11-14", "2020-09-23", "2020-12-12", "2020-12-10", "2020-09-24", "2020-12-07", "2020-06-13", "2020-08-12","2020-06-23", "2020-07-11", "2020-12-25", "2020-05-30", "2020-11-29", "2020-12-10", "2020-10-25", "2020-12-21", "2020-09-24", "2020-11-15")
df2 <- data.frame(User_ID, Visit_date) %>%
  mutate(Visit_date = ymd(Visit_date))

df3 <- df1 %>% inner_join(df2, by = "User_ID") %>%
  mutate(fdate30 = ymd(Visit_date) + days(30)) %>%
  mutate(ed_interval = interval(Visit_date, fdate30)) %>% 
  mutate(ed4w = Diagnosis_date %within% ed_interval) %>%
  filter(ed4w == "TRUE")

df1$ed4w <- df3$ed4w[match(df1$Event_ID, df3$Event_ID)]

df1$ed4w[is.na(df1$ed4w)] <- "FALSE"