5th dnd – Will this cause balance issues if I grant a character a free feat to balance his low ability scores?

He will leave the character undernourished

Typically, characters begin with a +3 or +4 modifier for their main statistic and +1 or +2 for their secondary statistics. The primary score of +3 redeems a lot, but depending on the class, low secondary abilities could be a major drawback. An exploit is nominally worth about one ASI, and your character needs two just for his character to be at the usual starting numbers.

In summary, this is manifested by the fact that the PC probably has less HP, misuse of its class capabilities using secondary skill scores and poor skills, while the PC will be more easily subject to enemy spells in because of its low overall scores and will likely have a low AC due to low dexterity. Fortunate is a good feat to compensate for low scores, but its impact is limited. The character can still perform well in certain situations requiring less jets, for example. support the magic, but is still quite weak compared to the expected character of their level.

Another way to compare this is by Human Variant who score slightly lower than more specialized races, but a free foot. The difference in abilities between them and a specialized breed represents only one point in their main attribute. It's closer to the true value of an exploit.

Use a point-of-purchase / standard chart

If you want a balanced party, do not run statistics. The standard table is a good and well assigned capacity score with high statistics reasonably concentrated but no total dump statistics. The purchase of points is also an option, but it tends to invite analysis to paralysis as it is easy to see as an optimization puzzle.

Give your players the opportunity to switch to the standard matrix now or during the game after a few sessions. You do not need to try to balance it with Lucky.