Remove atmega from programmer and install in LedLabs connect rx,tx,rst, and 0v from programmer output connectors and connect to LedLabs, program in usual way. When using this way rx on uno board connects to rx on led labs and similarly tx to tx.
If using usb to serial converter like FTDI232 tx then connects to rx on led labs and vice versa. The pins used on this device is 4 of the 6 DTR, TX, RX, 0V. VCC, CTS pins can be omitted. When this device is plugged in to the computers usb this provides the power VCC, the 0V of this device requires connecting to led labs for the common ground. The DTS or (reset) pin of this device requires a 100nf in series before it connects to the reset of led labs, then rx to tx, and tx to rx.