You're right to be concerned. Connecting only three phase conductors and the EGC to a generator on a 480V wye system is problematic and, in many cases, will not work correctly and could be dangerous. Here's a breakdown

Why the Neutral is (Almost Always) Necessary
Unbalanced Loads

Your lighting circuits, and even the transformer feeding your 120/208V panel, are almost certainly unbalanced. This means the current drawn on each phase is not equal. In a wye system, the neutral conductor is essential for carrying the unbalanced current back to the source (generator). Without it, voltage imbalances will occur.

Voltage Imbalances

Without the neutral to carry unbalanced current, the voltage on each phase of the 480V system will shift. Some phases might have higher-than-normal voltage, and others lower. This can damage equipment, especially sensitive electronics and lighting ballasts.

Transformer Issues

While your 480V primary transformer could potentially work briefly without a neutral in some very specific balanced load scenarios, it's highly discouraged. A Wye-connected transformer primary needs a neutral for proper operation, especially under unbalanced loads. Without a neutral, the magnetic core can become saturated, leading to overheating, noise, and potential failure of the transformer.

Generator Damage

Forcing the generator to supply an unbalanced load without a neutral return path can damage the generator's windings and control system.

Why It Might Seem to Work (Briefly or Partially) - but isn't Safe

There's a small possibility that some loads might appear to operate, temporarily, under certain conditions: Very Balanced Loads (Highly Unlikely)

If the 480V lighting loads are perfectly balanced across all three phases, and the 480-208 transformer is only lightly loaded, it might seem to work for a short period. However, perfect balance is virtually impossible to maintain in a real-world installation. Even small imbalances will cause problems.

Capacitive Coupling (Dangerous Illusion)

In some cases, there might be capacitive coupling to ground within the system. This could provide a false neutral path. This is highly dangerous because it is an unpredictable and unreliable path for neutral current. It could lead to elevated voltage on the EGC and create shock hazards.

Existing Grounding Connections (Never Intended for Neutral Return)

It's possible the system relies on grounding connections to try and provide a neutral path, but this is a very bad idea. The ground system is designed for fault current, not neutral current.

The Correct Solution1. Confirm the Generator's Configuration

Determine if the generator is wye-connected and designed to provide a neutral output. If it is, you

MUST run a neutral conductor from the generator to the transfer switch and connect it appropriately.2. Inspect the Transfer Switch

The transfer switch should have a lug or connection point for the generator neutral. Make sure it's properly sized and rated for the expected neutral current.3.

Neutral Bonding

Crucially, the neutral should only be bonded to ground at one point. Typically, this is at the service entrance (where the 480V utility power enters the building) or within the generator itself if it's designed to be a separately derived system.

Do NOT bond the neutral to ground at multiple locations, as this creates dangerous circulating ground currents.4. Verify Grounding

Ensure the grounding electrode system is properly installed and connected to the EGC.5.

Load Balancing

Check the load on the 480V lighting panels and try to balance the load as much as possible across the three phases to reduce the neutral current.6.

Consult an Electrical Engineer/Qualified Electrician

This is a complex situation. It's essential to have a qualified electrical engineer or licensed electrician review the entire system, verify the generator's specifications, ensure proper wiring, and perform testing before connecting a generator. This is not a DIY project.
In Summary:

Running a 480V wye system without a neutral from the generator is almost certainly a recipe for problems and potential hazards. You must* provide a properly sized and connected neutral conductor from the generator to the transfer switch and ensure correct bonding and grounding practices are followed. Have a qualified professional evaluate the system before attempting to use the generator. Flag for review