Most of a woman’s genital lubrication comes during arousal, not with orgasm (unless you're wondering about female ejaculation; there isn't agreement about whether this occurs for women, and if it does occur, most women aren't aware of it). And remember, most women can only achieve orgasm with direct clitoral stimulation; few women experience orgasm with penetration alone.
The amount of secretion--or vaginal lubrication--is most dependent on the time and energy and technique put into foreplay or arousal. After menopause, both arousal and lubrication are affected by the absence of estrogen in the genital tissues, which also decreases blood circulation.
Using a vaginal estrogen product (by prescription only) can allow a woman to produce more secretions on her own, which many women prefer. Talk to your health care provider about considering that as an option.
Non-hormonal (and non-prescription) options include vaginal moisturizers and lubricants. Moisturizers (like Replens or Yes) are used every few days and keep the vagina moist and supple; lubes are used at the time of sex to add comfort. The hybrid (Liquid Silk and Sliquid Silk) and silicone (Pink and Oceanus) lubes last somewhat longer than the water-based; water-based lubes may require re-application during a sexual encounter (which can itself be intimate).
Sharing with your partner what feels best to you will be helpful. Let your partner know that a lube is beneficial for your pleasure and find a way, together, to incorporate it in a tasteful, non-embarrassing--even arousing!--way.