No matter what tab length you choose, you will eventually run into a situation where your columns aren't aligned.
I know you want to do this via post-processing, but you should know that if you set SQLite's .mode option to columns, you'll get the kind of output you want. The column widths will adjust to the length of the longest row. Since you apparently don't want headers, there's a setting for that, too. So
.mode columns
.headers off
will do what you want. These settings will last through your entire session, no matter how many queries you make. Here's an example of real output from one of my databases:
Column-formatted SQLite output (click to expand/collapse)
JVI v. Universal Edward H. Rice 3823
Cevasco v. Amtrak, et al. Richard E. Snyder 3854
Bailey v. Chicago Jordan Marsh 3910
New York Crane Collapse Joseph DeDonato 3915
Elwood Fire David L. Laveck 3922
Logue v. ITW Benjeman L. Nichols 3923
Moradi v. Chicago Elizabeth A. Freidheim 3936
Torres v. McDermott Carol P. Woosley 3938
Petrielle v. Martin Plumbing Jeffrey T. Lahners 3940
3501 S. Francisco Elizabeth A. Freidheim 3951
Mwesigwa v. DAP Steve Heine 3970
Montrose Water Main Break John H. Ehrlich 3985
JCI Polycarbonate Pan Cracking Charles Obosu 3986
If you insist on post-processing, search for tools that reformat Markdown tables. The output you have is essentially Markdown.