Using a fixed oscillator to provide a clock signal for the data is a possibility, however it has a cost.
Whoever source the clock is the boss of timing, and everything else must comply with that timing.
If you use an external clock such as an oscillator (probably with some dividers), then the device sourcing the data must take that clock as an input and be sure that it always provides the data soon enough - which is to say a "setup time" before the active clock edge, plus any possibly clock skew between the source and destination. If you can make such a guarantee, it makes the job of designing the receiver very easy, since the receiver can add the requirement that the clock rate be steady.
Some devices such as digital-to-analog converters can have very harsh requirements for steadiness (formally, low jitter, or in communication terms, low phase noise) of the clock rate, and have their performance seriously impaired when that is not the case.
But other devices (especially those at relatively low rates and where data is just being received into a memory of some type - your LCD may be an example) can be perfectly fine with a clock that runs irregularlarly, for example in bursts. This can make the job of sourcing the data from software a lot easier, since the source can wait until it has data ready and present that data, before it activates the clock. With this type of interface, a very easy way of driving it from an older PC (at low to moderate data rates) was to use two data bits of the parallel port, and "bit bang" the data stream by explicitly asserting and de-asserting the clock and data signals in software. This would typically achieve the right relative timing (data valid before clock) but with a fair degree of variation in the overall timing. Unfortunately, this method does not work well with USB-connected I/O devices as the high latency of USB makes it slow, and it typically will not work at all with the data lines of USB-centronics printer adapters (though it may be possible with the control lines, or by acting more literally like a printer).