Here is a modern sounding lick which uses several fourth intervals.

We are in the key of C major and we use the D dorian mode here.
Playing scales in fourth intervals is a very good exercise for your left hand!

I use the neck pickup with a clean tone and some reverb. Of course, you could also add some overdrive!

E Blues

Here we mix E major and E minor pentatonic scales to get a typical Blues phrasing.

A nice and classic lick with a repetitive motif in E Major pentatonic in the beginning and the minor pentatonic scale at the end.
Try to begin the lick on the first or the third bar of a 12 bars Blues.

I use the Fulltone OCD pedal and the clean channel of the Mesa Boogie V-Twin preamp with some reverb added in pro tools.

Hot Country

Here's a cool lick using lots of open strings : It begins with a repetitve motif and ends with the G blues scale. I also use the chicken picking technique: the pick + middle finger

It's in the key of G and uses the G Blues scale.

Use the bridge pickup to get that classic country twang tone. Also use a compression pedal/plug-in with lots of compression because we want a highly "squished" sound. Add some reverb and a slap-back delay (100ms to 300ms with a single repeat).