Ciara -- Served with Lawsuit While on Stage!

Ciara's performance at LA Pride did not go as planned last night ... because she was served with legal papers right in the middle of her show!

As TMZ first reported ... The Factory, a popular West Hollywood club, sued the singer for bailing on a performance scheduled for Friday night. Ciara's people maintain they informed the club she could not be there, but they continued to promote her appearance anyway.

Since the club people knew exactly where Ciara was going to be Saturday night, they sent their process server right up to the stage to hand her the papers ... which she quickly tossed back.