If you only use 1 event per wheel revolution then you'd better not want precision for any time you are changing speed. And as Udo points out, wheel diameter does change. Think not? Check your tire wear and air pressure and weight of rider(s) and baggage -- but the difference will be a few % at most if you don't ride on flats.
If your speedometer is a solid roller that contacts the tire tread then you can get the real speed. If the roller is a timing wheel (has holes or spokes) then you can use a light bridge and measure movement in a small fraction of a wheel turn. If your roller generates even a small electric current you can measure that as an analog to your speed in about 1/10th of a millisecond (the ADC is that slow, yes, slow). Any of that would beat hell out of getting 1 read per about 4 meter wheel turn.
I've been wondering if having a magnet near the wheel rim (conductive rim only) would generate enough eddy current to measure as the wheel turns... sensing parts list: bracket, magnet, Hall sensor; zero moving parts. Or maybe... send a little juice to a coil next to the rim and as it induces current in the rim there will be a change in either the current draw in the coil or in the field it generates, nothing is free!
As to missing a sensor event, it's possible but do some math. At 63-64 kph a 700 cm bicycle wheel turns 4 times a second. That's 250 ms per turn. You can -easily- check a digital sensor 10x per millisecond and still do some math and bit-bang pins or ports if you use small, non-blocking code and stay away from slow operations. With interrupts you can get that event even more sure but do you need to? A magnet on a hub can be be sensed long enough to give several reads before it passes, even at speed.
Interrupts have an effect on the timers, they stop while the ISR is running. If it's just a few microseconds then the effect is less than 1% but there it is, nothing's perfect.
Maybe the best would be to use 2 Tinys. One to watch the wheel and one to run the LCD. But don't use regular serial between them for communication, they do support SPI and I2C. Send digital data 1 byte at a time and the watcher will not have to look away for more than a few microseconds at a time.