Yes, you can plant them in spring. Many bulb suppliers will ship both in fall and spring. The bulbs are usually dug up in early fall then shipped out. If not, they are refrigerated then shipped out in spring. If planted immediately aftter arrival in spring, they'll bloom the same year.

Those lilies that are sold in bloom in spring will not bloom again until the following year. My lilies bloom only once a year. I've read that there are some repeat bloomers, but I have not tried any.

Seems to me if planted in Fall the lilies always bloom that summer. Planted in Spring the lily will bloom late if at all the first summer. The following summer that Spring planted lily will take off & do good from that point on.
It is a matter of root system. A Fall planted lily has much more time to establish it roots to bloom the first summer. The Spring planted lily has to get roots established before it can do much. Also the size of the bulb plays into the picture. Small bulbs take longer to establish roots. Also I am speaking from zone 5 it may be different in warm climates.

I've planted many lilies in the "early spring" and gotten some blooms , they'll bloom from then on. Be patient with them it just gets better!