“Can”? Most definitely.
Listen, Lions and Tigers are both exceptionally fast and explosive predators. They have just about every single advantage on the ostrich.
But Ostriches aren’t just the fastest birds, they are the fastest two-legged runners in the animal kingdom, now, an exceptionally quick lioness would probably catch an ostrich if they were in a straight line race.
Here are some statistics:
Male lions can run at speeds of up to 35mph – females are faster
Male tigers can run at speed of up to 35mph – females are faster
Ostriches can top out at about 43mph
So, in a straight line. A particularly quick tiger/lion could catch the ostrich, however ostriches can maintain those speeds for a longer time than either cat. And they always have a fairly big headstart on the cat.
Ostriches have exceptional vision, and they will notice the large predator very early – before they get close enough to pose a chasing threat.
If you’re not a cheetah, running down an ostrich is very difficult.

An ostrich can complete a 42 km full marathon in 35 to 45-minutes, as compared to men’s world record time of 2:00:35, set by Kenyan athlete, Kelvin Kiptum, on October 8, 2023, at the 2023 Chicago Marathon.
It can cruise at an unfaltering 50 km/h for enormous distances, and hurtle full throttle at 70 km/h for shorter ones, bounding 3 -4.9 m with each stride.
Their long neck, with 17 vertebrae, combined with their excellent vision, enables them to spot predators from afar.
Despite inhabiting some of Africa’s driest regions, ostriches are adept and fearless swimmers, using their buoyant bodies and strong legs to propel themselves in water. They negotiate water bodies similarly to water birds, though their non- webbed feet are better suited to land. The birds can handle reasonably strong currents and are often known to enter shallows, particularly calm inland waters like lakes and streams, to cool off or evade threat.
Despite their formidable stamina, strength and superior endowments, ostriches which inhabit the African savanna, face grave threat from lions, leopards, jackals, wild dogs, cheetahs, spotted hyenas, and Nile crocodiles. Other predators like jackals, warthogs, mongooses, Egyptian vultures, and various birds of prey target ostrich eggs, chicks, and juveniles.
There are no tigers in their native ranges but if there were one the feathered giant could easily outrun it.
As for lions, while an individual bird can outrun a single animal but a group hunting together can tire it out and arrange themselves a satisfying snack.