When performing a climb in a SIAI-Marchetti SF.260 with a Lycoming engine, the fuel pressure decreased. Why would that happen?
The most obvious answer is "Gravity".
To some extent this is "normal" in a low-wing aircraft with a nose-mounted engine and a fuel pump drawing fuel from the wing tanks into the engine: As the nose pitches up the fuel needs to run "uphill" to get to the engine - that's more work for the fuel pump, which might not maintain full "straight-and-level" fuel pressure.
You can see something similar in a Piper Cherokee in an aggressive climb, particularly if you are only using the engine-driven (mechanical) fuel pump: The fuel pressure typically drops when you pitch past ~15-20 degrees nose-up. The drop isn't much, but it's noticeable if you're looking for it.
If the pressure drop makes you uncomfortable turning on the electric boost pump(s) may reduce or eliminate it, but as long as the fuel pressure remains in the aircraft's normal operating range it's probably not a cause for concern. You should however become familiar with how much the pressure tends to drop in a climb: A larger drop than "normal" may indicate a problem with the (mechanical) fuel pump which you would want to have your mechanic investigate.