I do not have any experience with the MicroBlaze.
As far as I understand it’s a controller (library) which can be run on a FPGA!?
You also didn’t write what your LCD would be (width, height, color), a ‘smart’ or a ‘dump’ display.
From your question it seems to me, you want to use a ‘dump’ display, which means directly connected to the controller.
For the the STM controllers (STM32F4/7 and -H7) this is possible as these controllers have special hardware build in. When using these controllers with direct LCD driving you need also appropriate memory as frame buffer. When using smaller resolutions and color depth (320 x 240 x 16-bit = 153600), this might fit into the controllers internal SRAM. For larger resolutions you need an external (mostly SDRAM) RAM.
Does the MicroBlaze allow direct driving of a dot matrix LCD? I did not find any information about this.
The most easy way is using a ‘smart’ display which has it’s own display driver and frame buffer.
These kind of displays can be either filled via SPI transfer or via 8-bit or 16-bit parallel IO/memory transfer.
Independent of what you use, you just have to write a flush_cb function which transfers the content of the lvgl’s working buffer to the real frame buffer (controller internal or extern on display)