Read numbers from control file and Extract matching line numbers from the data file

You could use awk for this I believe like so:

awk -vN=3 '/PATTERN/ {skips[FNR+N]=1;} {if(!(FNR in skips)) print;}' <file>

so each time we hit PATTERN we'll record the line that is N away from here, and only print those lines we have not marked for skipping.

with gawk you could use -i inplace as well to do it in place

As you noted, that wouldn't handle multiple files. Of course, you could wrap with a for loop to iterate over all the files, but if there aren't enough to make the commandline too long you could also do it like so:

 awk -vN=3 '{if(FNR==1) split("", skips, ":");} /PATTERN/ {skips[FNR+N]=1;} {if(!(FNR in skips)) print;}' *

where we reset skips to an empty array each time FNR hits 1, so the start of each file.
With gnu awk you could write it as:

gawk -i inplace 'FNR==1{delete nr};/PATTERN/{nr[FNR+3]++};!(FNR in nr)' file*

Using awk:

awk '/logical IO/ {if (!seen) {print; seen=1}; next}; {print; seen=0}' file.txt 

• /logical IO/ {if (!seen) {print; seen=1}; next} checks if the line contains logical IO, if found and the variable seen is false i.e. previous line does not contain logical IO, then print the line, set seen=1 and go to the next line else go to the next line as the previous line has logical IO

• For any other line, {print; seen=0}, prints the line and the sets seen=0

Example:

$ cat file.txt 
select * from test1 where 1=1
testing logical IO 24
select * from test2 where condition=4
parsing logical IO 45
testing logical IO 500
select * from test5 where 1=1
testing logical IO 24
select * from test5 where condition=78
parsing logical IO 346
parsing logical IO 346
testing logical IO 12

$ awk '/logical IO/ {if (!seen) {print; seen=1}; next}; {print; seen=0}' file.txt 
select * from test1 where 1=1
testing logical IO 24
select * from test2 where condition=4
parsing logical IO 45
select * from test5 where 1=1
testing logical IO 24
select * from test5 where condition=78
parsing logical IO 346