> df = data.frame(
+     line1 = sample(LETTERS, 5),
+     line2 = sample(LETTERS, 5),
+     line3 = sample(LETTERS, 5)
+ )
> df
  line1 line2 line3
1     P     T     P
2     B     H     A
3     A     F     C
4     K     P     N
5     G     L     Y
> library(dplyr)
> library(tidyr)
> library(tibble)
> as.data.frame(t(df)) %>%
+     rownames_to_column(var = "Gene") %>%
+     gather(value,variable,-Gene) %>%
+     spread(variable,value)  %>%
+     mutate_at(vars(-Gene), funs ( ifelse ( is.na(.), 0, 1)))
   Gene A B C F G H K L N P T Y
1 line1 1 1 0 0 1 0 1 0 0 1 0 0
2 line2 0 0 0 1 0 1 0 1 0 1 1 0
3 line3 1 0 1 0 0 0 0 0 1 1 0 1
Warning message:
attributes are not identical across measure variables;
they will be dropped 

cpad already answered it, but here's an answer using more contemporary tidyverse syntax.

example data.

df <- structure(list(LINE1 = c("A", "B", "C", NA, NA), LINE2 = c("B", 
"D", "E", "F", NA), LINE3 = c("C", "D", "G", "H", "I")), class = c("tbl_df", 
"tbl", "data.frame"), row.names = c(NA, -5L))

# A tibble: 5 × 3
  LINE1 LINE2 LINE3
  <chr> <chr> <chr>
1 A     B     C    
2 B     D     D    
3 C     E     G    
4 NA    F     H    
5 NA    NA    I

Tidyverse solution.

library("tidyr")
library("dplyr")

df |>
  pivot_longer(everything()) |>
  drop_na() |>
  mutate(binary=1L) |>
  pivot_wider(names_from=value, values_from=binary, values_fill=0L)

# A tibble: 3 × 10
  name      A     B     C     D     E     G     F     H     I
  <chr> <int> <int> <int> <int> <int> <int> <int> <int> <int>
1 LINE1     1     1     1     0     0     0     0     0     0
2 LINE2     0     1     0     1     1     0     1     0     0
3 LINE3     0     0     1     1     0     1     0     1     1

Using base stack and table (example data is from rpolicastro answer):

as.data.frame.matrix(table(stack(df)))
#   LINE1 LINE2 LINE3
# A     1     0     0
# B     1     1     0
# C     1     0     1
# D     0     1     1
# E     0     1     0
# F     0     1     0
# G     0     0     1
# H     0     0     1
# I     0     0     1