When you start to play leads most likely you'll begin with the blues scale played in the position of your bar chord. This means that if you start with a G chord you'll probably play in the position of the 3rd fret. When the chord changes to C you'll do the same forms starting on the 8th fret.
An alternative to doing that which gives your lead phrasing a different sound and feel is to work off a different position altogether. An altered major scale without the 7th and 4th of the scale is a common variation for lead playing. In the key of A start with your index finger on the 2nd fret (F#), then go to your pinky on the 5th fret (A). On the A string the notes are B on the second fret and C# on the fourth fret. Use your index and ring finger for these notes. Repeat the exact same fingerings on the D string for the notes E and F#, and again on the G string to get the notes A and B. On the B string the notes are C# and E on the 2nd and 5th frets followed by F# and A on the high E string, also played on the 2nd and 5th frets. A nice bluesy touch can be gotten by hitting a C note and bending it to C#.
Here's a riff based on this scale. Fret the E and A notes vvith your pinky on the B and E strings 5th fret. Pluck the two notes together with your middle and ring finger while holding the pick between your thumb and index fingers. Almost simultaneously, play the 4th fret G string pre-bent up a whole step to C#. In a continuous motion, bend back down to B and pull-off to the index finger waiting on the 2nd fret (A). Continue ta pull off to the open G string, then follow with a 4th to 2nd fret pull-off on the D string. End with your middle finger on the 3rd fret A string. Pull that note (C) and let it pop off to the open A string. A good place for this riff is in the 11th bar of a 12-bar blues progression, just before you go to the final V chord, in this case an E.