In a regular SQLite INSERT or UPDATE you can escape a single quote by adding another one.
Or if you are able to use a "parameter" insert, as it is possible with B4A, then you do not need to worry - the single quote will be accepted.
sql.ExecNonQuery2(INSERT INTO mytable VALUES (?,?), Array as Object(data1,data2))
The single quote escape way is for SQLite in any language. I sometimes write a little subroutine to replace all single quotes with 2 single quotes and then wrap the string with a quote at each end, ready for SQLite.