Lap belts were available when your car was new. They are better than nothing, in fact more than 50% as effective as today's shoulder belts.
To keep an authentic look, if you can find an old set of accessory belts, get new webbing straps installed the old material weakens over time, in fact belts have an effective life of about 10 years before they lose their resiliency.
When your car was new some guys even installed war surplus airplane seat belts.
They were rare but they were available as an accessory. Nobody installed them as standard equipment. Tucker was going to, in 1948, but never did.