Ok, it looks like I figured out how to achieve the desired mixed configuration in subject, but manually.
In Peripherals Config Tool, I configured LPUART in eDMA mode and disabled "Enable RX eDMA channel" flag, then I specified my own "transfer callback function name" in "LPUART eDMA handle" section to catch when Tx DMA transfer finishes.
To start queueing data in FreeRTOS queue through Rx interrupt mode, I then had to manually enable Rx interrupt:
LPUART_EnableInterrupts(LPUART1, kLPUART_RxDataRegFullInterruptEnable);
Then I had to implement my own LPUART1_IRQHandler() to fill the Rx FreeRTOS queue with received data:
uint8_t temp = LPUART_ReadByte(LPUART1);
xStreamBufferSendFromISR(rxQueue, (void*)&temp, 1, &xHigherPriorityTaskWoken);
Another very annoying thing is that I had to manually add ISR priority initialization to avoid FreeRTOS to get stuck because of priority too high by manually calling after peripheral initialization:
NVIC_SetPriority(DMA0_DMA16_IRQn, 5);
NVIC_SetPriority(LPUART1_IRQn, 5);
since it looks there's no way to specify them from Config Tool.
Suggestions to improve the above workflow, which honestly I don't like so much?