Without using glitches, no. It is not possible to obtain both T & S level 2 & 3 techs from the same move tree. Techs that seem obtainable because you are on the correct side of the T/S bar and have the prerequisites for unlocking them appear blue on the tech screen.
Using your example, you might see this case:
- Lloyd learns Fierce Demon Fang, since he has used Demon Fang 50+ times and is on the Strike side of the spectrum.
- Later on in the game (or in a subsequent playthrough), you decide to switch Lloyd's skills/items so he is in the Technical spectrum.
- You should see Double Demon Fang on the tech page in blue. To learn it, you'll need to forget the Strike equivalent lvl.2 arte, which would be Fierce Demon Fang.
This is described as such in this big FAQ post, specifically looking at the How do I learn techs that are in blue? section. As Fambida mentioned in his comment, there is a 'Tech Glitch' that involves switching the user you are trying to glitch with out of the first party spot, and setting an arte shortcut for that user. This allows them to learn both S&T type, and adds some implications to how you can chain these artes together.