Bmeitxh

Absolutely not safe.

Those trusses were engineered with a heavy dependency on the bottom chords, which are in tension. Removal has left them extremely vulnerable to collapse due to spreading, especially under snow loads, but also under just the load of the roof itself. The roof system is basically a hinge now.

To get a good mental image, picture yourself standing on an ice rink and sliding your feet outward. How far do you get before your groin starts to scream at you?

Best case scenario, that ridge slowly sags over the opening and looks ridiculous. It will push walls around with it, cracking drywall and binding windows. Worst case, full collapse. Death. Destruction. Worst of all, humiliation.

Repair will require new lumber installed with a suitably fastening system, such as construction adhesive and through-bolts. It may be necessary to winch the walls back into alignment first if sagging has already begun.

With no bracing above, you might want to check the out side walls - they are probably already spreading. Once they start moving the stabilization and repair can cost many thousands if the roof stays in place, tens of thousands if it comes down.

There are ways to mitigate the damage done, but it needs to be done now before the walls spread, the rafters move and the roof leaks if not collapses. Yes I have seen bonehead DIY hacks like this.

Steel plates in the outside walls with cables to pull the walls back together, repair the damage to the rafters, new bracing with some engineered cables added.

I would suggest getting the bracing and cable system installed now or it will cost much more than the lift and the loss of use if the root comes down.

The triangle is an extremely stable form of architecture precisely because it has three sides. You remove one side, and you have one of the least stable forms of architecture on account that two members connected at a point can be affected by torque, which is by definition a force multiplier. If you want to play around with it to get a sense, try gluing two Popsicle sticks and three Popsicle sticks like the design in the picture above.

Any force directed downward will because of the elasticity of the wood create force outwards. If the members were steel, there would be substantially less deformation resulting in less outward force, but lumber is relatively flexible.

Now, it should be noted that some of the horizontal members are still in place, as many as half, and those runs will make it unlikely the structure will collapse under normal conditions, however, heavy winds or heavy snowfall, as mentioned in other comments, likely to create outward stresses in the middle section of the structure. The exact details of what will happen will largely be a matter of detail. To some extent, existing construction code generally overengineers a solution to ensure that minor failure will not result in human harm.

It is possible to create both the space needed to elevate the car, and have a structurally sound garage given the picture. For instance, additional chords can be installed low enough to recreate trusses, but high enough to accommodate a raised vehicle. There are a number of truss styles that do not use a horizontal bottom chord, the scissor truss for instance. And using steel as a construction material can help to redirect the tensions through materials more capable of absorbing the load. Lastly, the walls themselves can be modified. It was typical of cathedrals to buttress on the exterior, the wall to handle high-arching ceilings, for instance.

Construction is often a question of engineering as much as it is design, and if safety is a concern, such as it might be in this photo, consulting a structural engineer would be the right thing to do. Structural design is their expertise, which would be my recommendation.