It will leave the character underpowered
Usually characters start with a +3 or +4 modifier to their primary stat and +1 or +2 for their secondary stats. The primary score of +3 redeems a lot, but depending on the class, the low secondary abilities might be a significant drawback. A feat is nominally worth about one ASI, and your character needs two just to get their character to be at the usual starting numbers.
In a nutshell, this manifests as the PC likely having less HP, bad use of their class abilities using secondary ability scores and bad skills, while the PC will be more easily subject to enemy spells because of their overall low scores and will likely have a low AC because of poor Dexterity. Lucky is mechanically a good feat to compensate low scores, but its impact is limited. The character may still perform well in some situations that require less rolls, eg. support magic, but is still pretty weak compared to the expected character of their level. Do note that support magic tend to require concentration, effectively limiting the possibility of basing a character around just support magic.
Another way to compare this is through Variant Humans who gain slightly worse ability scores than more specialized races but instead one free feet. The difference in abilities between them and a specialized race is just a single point in their primary attribute. That's closer to the true value of a feat.
Use point buy/standard array
If you want a balanced party, don't roll for stats. The standard array is a good, well-rounded assignment of ability scores with reasonably focused high stats but no totally dump stats. Point buy is also an option, but it tends to invite analysis-paralysis to some players because it's easy to see as an optimization puzzle.
Give your players the option to switch to the standard array now or during the game after a few sessions, and you don't need to try balancing it with Lucky.