The -v option to grep inverts the search, reporting only the lines that don't match the pattern.
Since you know how to use grep to find the lines to be deleted, using grep -v and the same pattern will give you all the lines to be kept. You can write that to a temporary file and then copy or move the temporary file over the original.
grep -v pattern original.file > tmp.file
mv tmp.file original.file
You can also use sed, as shown in shellfish's answer.
There are multiple possible refinements for the grep solution, but for most people most of the time, what is shown is more or less adequate (it would be a good idea to use a per process intermediate file name, preferably with a random name such as the mktemp command gives you). You can add code to remove the intermediate file on an interrupt; suppress interrupts while moving back; use copy and remove instead of move if the original file has multiple hard links or is a symlink; etc. The sed command more or less works around these issues for you, but it is not cognizant of multiple hard links or symlinks.