foo
bar
foobar
barfoo
last
line

foo
bar
foobar

$ tac file | sed '1,3d' | tac
foo
bar
foobar

$ tac file | awk 'NR==1{next}NR==2{next}NR==3{next}1' | tac
foo
bar
foobar

... | awk '{l[NR] = $0} END {for (i=1; i<=NR-3; i++) print l[i]}'

... | awk '{if (a) print a; a=b; b=c; c=$0}'

awk -v n=$(($(wc -l < file) - 3)) 'NR<n' file

$ seq 6 | head -n-3
1
2
3

awk 'NR>n{print A[NR%n]} {A[NR%n]=$0}' n=3 file

Line 1 -> A[1]
Line 2 -> A[2]
Line 3 -> A[0]
Line 4 -> A[1]
Line 5 -> A[2]
...

awk '{if(NR==FNR){c++}else if(FNR<=c-3){print}}' file file

for i in {500000..1000000}; do
    echo "The quick brown fox jumped over the lazy dog $i" >> file;
done

$ for i in {1..10}; do (
    time awk '{if(NR==FNR){c++}else if(FNR<=c-3){print}}' file file > /dev/null ) 2>&1 |
       grep -oP 'real.*?mK[d.]+';
  done | awk '{k+=$1}END{print k/10" seconds"}';
0.4757 seconds

$  for i in {1..10}; do (
    time awk '{l[NR] = $0} END {for (i=1; i<=NR-3; i++) print l[i]}' file > /dev/null ) 2>&1 |
        grep -oP 'real.*?mK[d.]+';
   done | awk '{k+=$1}END{print k/10" seconds"}';
0.5347 seconds

head -n -3