It's due to E. coli's lac operon breaking down the lactose into glucose/galactose, which then get broken into acidic end products that drop the pH of the surrounding medium. MacConkey agar contains Neutral Red which turns a bright pink/red at acidic pH. Lac- E. coli won't digest the lactose and will eventually start to make the pH somewhat alkaline (which turns Neutral Red yellow) by breaking down peptides.
What strain are you working with? If it's a lab strain it's usually pretty easy to find out, because their genotypes have already been characterized. For example Top10/DH10B have the Δ lacX74 mutation where the whole lac operon is gone.
If it's a wild-type E. coli strain that happens to be lac-, then there's two ways of maybe figuring that out:
Just get the operon sequenced and look for mutations in either LacZ (B-galactosidase) or LacY (permease) or their promoter. I think LacZ and LacY are the only parts of the operon that actually contribute to the Lac+ phenotype (but I could be wrong on that). If the entire genome of the strain has already been sequenced then just look that up.
Less informative way: Test it for the ability to turn a culture containing ortho-Nitrophenyl-β-galactoside (ONPG) and Isopropyl β-D-1-thiogalactopyranoside (IPTG) yellow. ONPG is a lactose analog that can freely cross the membrane even without a transporter (but it doesn't induce the lac operon on its own, hence the IPTG) that turns yellow when broken down by B-galactosidase. If you get a phenotype where it can't digest lactose but turns ONPG + IPTG cultures yellow then there's likely a mutation in lacY but lacZ is still present and active, lactose just can't enter the cells. If it's negative then lacZ is inactive (though you won't know why if that's due to just a mutation in LacZ, the whole operon missing, etc.)